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1. Borichev, A. et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt587",{id:"formSmash:items:resultList:0:j_idt587",widgetVar:"widget_formSmash_items_resultList_0_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hedenmalm, HåkanKTH, Superseded Departments, Mathematics.Volberg, A.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index2004In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 207, no 1, p. 111-160Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:0:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_0_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate non-trivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. Chanillo, S. et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt587",{id:"formSmash:items:resultList:1:j_idt587",widgetVar:"widget_formSmash_items_resultList_1_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Helffer, B.Laptev, AriKTH, Superseded Departments, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nonlinear eigenvalues and analytic hypoellipticity2004In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 209, no 2, p. 425-443Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:1:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_1_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non-self-adjoint operators has a nonzero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 3. Gustafsson, Björn PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt584",{id:"formSmash:items:resultList:2:j_idt584",widgetVar:"widget_formSmash_items_resultList_2_j_idt584",onLabel:"Gustafsson, Björn ",offLabel:"Gustafsson, Björn ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt587",{id:"formSmash:items:resultList:2:j_idt587",widgetVar:"widget_formSmash_items_resultList_2_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, Superseded Departments, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Putinar, M.Shapiro, H. S.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Restriction operators, balayage and doubly orthogonal systems of analytic functions2003In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 199, no 2, p. 332-378Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:2:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_2_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Systems of analytic functions which are simultaneously orthogonal over each of two domains were apparently first studied in particular cases by Walsh and Szego, and in full generality by Bergman. In principle, these are very interesting objects, allowing application to analytic continuation that is not restricted (as Weierstrassian continuation via power series) either by circular geometry or considerations of locality. However, few explicit examples are known, and in general one does not know even gross qualitative features of such systems. The main contribution of the present paper is to prove qualitative results in a quite general situation. It is by now very well known that the phenomenon of double orthogonality is not restricted to Bergman spaces of analytic functions, nor even indeed has it any intrinsic relation to analyticity; its essence is an eigenvalue problem arising whenever one considers the operator of restriction on a Hilbert space of functions on some set, to a subset thereof, provided this restriction is injective and compact. However, in this paper only Hilbert spaces of analytic functions are considered, especially Bergman spaces. In the case of the Hardy spaces Fisher and Micchelli discovered remarkable qualitative features of doubly orthogonal systems, and we have shown how, based on the classical potential-theoretic notion of balayage, and its modern generalizations, one can deduce analogous results in the Bergman space set-up, but with restrictions imposed on the geometry of the considered domains and measures; these were not needed in the Fisher-Micchelli analysis, but are necessary here as shown by examples. From a more constructive point of view we study the Bergman restriction operator between the unit disk and a compactly contained quadrature domain and show that the representing kernel of this operator is rational and it is expressible (as an inversion followed by a logarithmic derivative) in terms of the polynomial equation of the boundary of the inner domain.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 4. Haimi, Antti PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt584",{id:"formSmash:items:resultList:3:j_idt584",widgetVar:"widget_formSmash_items_resultList_3_j_idt584",onLabel:"Haimi, Antti ",offLabel:"Haimi, Antti ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bulk asymptotics for polyanalytic correlation kernels2014In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 266, no 5, p. 3083-3133Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:3:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_3_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For a weight function Q : C -> R and a positive scaling parameter in, we study reproducing kernels K-q,K-mQ,K-n of the polynomial spaces A(q,mQ,n)(2) :=span(C) {(z) over bar (-r) z(j) vertical bar 0 <= r <= q-1, 0 <= j <= n-1} equipped with the inner product from the space L-2 (e(-mQ(z)) dA(z)). Here dA denotes a suitably normalized area measure on C. For a point z(0) belonging to the interior of certain compact set S and satisfying Delta Q (z(0)) > 0, we define the resealed coordinates z = z(0) + xi/root m Delta Q(z(0)), w=z(0) + lambda/root m Delta Q(z(0)). The following universality result is proved in the case q = 2: 1/m Delta Q(z(0))vertical bar K-q,K-mQ,K-n(z,w)vertical bar e(-1/2mQ(z)-1/2mQ(w)) -> vertical bar L-q-1(1) (vertical bar xi - lambda vertical bar(2))vertical bar e(-1/2 vertical bar xi-lambda vertical bar 2) as m,n -> infinity while n >= m - M for any fixed M > 0, uniformly for (xi,lambda) in compact subsets of C-2. The notation L-q-1(1) stands for the associated Laguerre polynomial with parameter 1 aid degree q - 1. This generalizes a result of Ameur, Hedenmalm and Makarov concerning analytic polynomials to bianalytic polynomials. We also discuss how to generalize the result to q > 2. Our methods include a simplification of a Bergman kernel expansion algorithm of Berman; Bemdtsson and Sjostrand in the one compex variable setting, and extension to the context of polyanalytic functions. We also study off-diagonal behaviour of the kernels K-q,K-mQ,K-n.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. Haimi, Antti PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt584",{id:"formSmash:items:resultList:4:j_idt584",widgetVar:"widget_formSmash_items_resultList_4_j_idt584",onLabel:"Haimi, Antti ",offLabel:"Haimi, Antti ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt587",{id:"formSmash:items:resultList:4:j_idt587",widgetVar:"widget_formSmash_items_resultList_4_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hedenmalm, HåkanKTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Asymptotic expansion of polyanalytic Bergman kernels2014In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 267, no 12, p. 4667-4731Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:4:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_4_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider the q-analytic functions on a given planar domain Omega, square integrable with respect to a weight. This gives us a q-analytic Bergman kernel, which we use to extend the Bergman metric to this context. We recall that f is q-analytic if (partial derivative) over bar (q) f = 0 for the given positive integer q. Polyanalytic Bergman spaces and kernels appear naturally in time-frequency analysis of Gabor systems of Hermite functions as well as in the mathematical physics of the analysis of Landau levels.

We obtain asymptotic formulae in the bulk for the q-analytic Bergman kernel in the setting of the power weights e(-2mQ), as the positive real parameter m tends to infinity. This is only known previously for q = 1, by the work of Tian, Yau, Zelditch, and Catlin. Our analysis, however, is inspired by the more recent approach of Berman, Berndtsson, and Sjostrand, which is based on ideas from microlocal analysis.

We remark here that since a q-analytic function may be identified with a vector-valued holomorphic function, the Bergman space of q-analytic functions may be understood as a vector-valued holomorphic Bergman space supplied with a certain singular local metric on the vectors. Finally, we apply the obtained asymptotics for q = 2 to the bianalytic Bergman metrics, and after suitable blow-up, the result is independent of Q for a wide class of potentials Q. We interpret this as an instance of geometric universality.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 6. Hedenmalm, Håkan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt584",{id:"formSmash:items:resultList:5:j_idt584",widgetVar:"widget_formSmash_items_resultList_5_j_idt584",onLabel:"Hedenmalm, Håkan ",offLabel:"Hedenmalm, Håkan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, Superseded Departments, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Outer functions of several complex variables1988In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 80, p. 9-15Article in journal (Refereed)7. Hedenmalm, Håkan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt584",{id:"formSmash:items:resultList:6:j_idt584",widgetVar:"widget_formSmash_items_resultList_6_j_idt584",onLabel:"Hedenmalm, Håkan ",offLabel:"Hedenmalm, Håkan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, Superseded Departments, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Spectral properties of invariant subspaces in the Bergman space1993In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 116, p. 441-448Article in journal (Refereed)8. Hedenmalm, Håkan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt584",{id:"formSmash:items:resultList:7:j_idt584",widgetVar:"widget_formSmash_items_resultList_7_j_idt584",onLabel:"Hedenmalm, Håkan ",offLabel:"Hedenmalm, Håkan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt587",{id:"formSmash:items:resultList:7:j_idt587",widgetVar:"widget_formSmash_items_resultList_7_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, Superseded Departments, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Borichev, AlexanderPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Approximation in a class of Banach algebras of quasianalytically smooth analytic functions1993In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 115, p. 359-390Article in journal (Refereed)9. Hedenmalm, Håkan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt584",{id:"formSmash:items:resultList:8:j_idt584",widgetVar:"widget_formSmash_items_resultList_8_j_idt584",onLabel:"Hedenmalm, Håkan ",offLabel:"Hedenmalm, Håkan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt587",{id:"formSmash:items:resultList:8:j_idt587",widgetVar:"widget_formSmash_items_resultList_8_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Shimorin, SergueiKTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).Sola, AlanKTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Norm expansion along a zero variety2008In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 254, p. 1601-1625Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:8:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_8_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The reproducing kernel function of a weighted Bergman space over domains in C-d is known explicitly in only a small number of instances. Here, we introduce a process of orthogonal norm expansion along a subvariety of (complex) codimension 1, which also leads to a series expansion of the reproducing kernel in terms of reproducing kernels defined on the subvariety. The problem of finding the reproducing kernel is thus reduced to the same kind of problem when one of the two entries is on the subvariety. A complete expansion of the reproducing kernel may be achieved in this manner. We carry this out in dimension d = 2 for certain classes of weighted Bergman spaces over the bidisk (with the diagonal z(1) = z(2) as subvariety) and the ball (with z(2) = 0 as subvariety), as well as for a weighted Bargmann-Fock space over C-2 (with the diagonal z(1) = z(2) as subvariety).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Hedenmalm, Håkan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt584",{id:"formSmash:items:resultList:9:j_idt584",widgetVar:"widget_formSmash_items_resultList_9_j_idt584",onLabel:"Hedenmalm, Håkan ",offLabel:"Hedenmalm, Håkan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt587",{id:"formSmash:items:resultList:9:j_idt587",widgetVar:"widget_formSmash_items_resultList_9_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). St Petersburg State Univ, Dept Math & Mech, 28 Univ Ski Pr, St Petersburg 198504, Russia..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stolyarov, D. M.Michigan State Univ, Dept Math, E Lansing, MI 48824 USA.;St Petersburg State Univ, PL Chebyshev Res Lab, St Petersburg, Russia.;Russian Acad Sci PDMI RAS, St Petersburg Dept Steklov Math Inst, Moscow, Russia..Vasyunin, V. I.St Petersburg State Univ, Dept Math & Mech, 28 Univ Ski Pr, St Petersburg 198504, Russia.;Russian Acad Sci PDMI RAS, St Petersburg Dept Steklov Math Inst, Moscow, Russia..Zatitskiy, P. B.St Petersburg State Univ, PL Chebyshev Res Lab, St Petersburg, Russia.;Russian Acad Sci PDMI RAS, St Petersburg Dept Steklov Math Inst, Moscow, Russia.;PSL Res Univ, Ecole Normale Super, CNRS, Dept Math & Applicat, Paris, France..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Sharpening Holder's inequality2018In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 275, no 5, p. 1280-1319Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:9:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_9_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We strengthen Holder's inequality. The new family of sharp inequalities we obtain might be thought of as an analog of the Pythagorean theorem for the L-p-spaces. Our treatment of the subject matter is based on Bellman functions of four variables.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Hoffmann-Ostenhof, M. et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt587",{id:"formSmash:items:resultList:10:j_idt587",widgetVar:"widget_formSmash_items_resultList_10_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hoffmann-Ostenhof, T.Laptev, AriKTH, Superseded Departments, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A geometrical version of Hardy's inequality2002In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 189, no 2, p. 539-548Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:10:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_10_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We prove a version of Hardy's type inequality in a domain Omega subset of R-n which involves the distance to the boundary and the volume of Omega. In particular, we obtain a result which gives a positive answer to a question asked by H. Brezis and M. Marcus.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 12. Hynd, R. et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt587",{id:"formSmash:items:resultList:11:j_idt587",widgetVar:"widget_formSmash_items_resultList_11_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lindgren, ErikKTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Approximation of the least Rayleigh quotient for degree p homogeneous functionals2017In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 272, no 12, p. 4873-4918Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:11:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_11_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present two novel methods for approximating minimizers of the abstract Rayleigh quotient Φ(u)/‖u‖p. Here Φ is a strictly convex functional on a Banach space with norm ‖⋅‖, and Φ is assumed to be positively homogeneous of degree p∈(1,∞). Minimizers are shown to satisfy ∂Φ(u)−λJp(u)∋0 for a certain λ∈R, where Jp is the subdifferential of 1p‖⋅‖p. The first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy ∂Φ(uk)−Jp(uk−1)∋0(k∈N). The second method is based on the large time behavior of solutions of the doubly nonlinear evolution Jp(v˙(t))+∂Φ(v(t))∋0(a.e.t>0) and more generally p-curves of maximal slope for Φ. We show that both schemes have the remarkable property that the Rayleigh quotient is nonincreasing along solutions and that properly scaled solutions converge to a minimizer of Φ(u)/‖u‖p. These results are new even for Hilbert spaces and their primary application is in the approximation of optimal constants and extremal functions for inequalities in Sobolev spaces.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. Hynd, Ryan et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt587",{id:"formSmash:items:resultList:12:j_idt587",widgetVar:"widget_formSmash_items_resultList_12_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lindgren, ErikKTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Approximation of the least Rayleigh quotient for degree p homogeneous funetionals2017In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 272, no 12, p. 4873-4918Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:12:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_12_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present two novel methods for approximating minimizers of the abstract Rayleigh quotient Phi(u)/parallel to u parallel to(p). Here Phi is a strictly convex functional on a Banach space with norm parallel to center dot parallel to, and Phi is assumed to be positively homogeneous of degree p is an element of (1,infinity). Minimizers are shown to satisfy partial derivative Phi(u) - lambda j(p)(u) there exists 0 for a certain lambda is an element of R, where J(p) is the subdifferential of 1/p parallel to center dot parallel to(p.) The first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy partial derivative Phi(u(k)) - j(p()u(k-1)) there exists 0 (k is an element of N) The second method is based on the large time behavior of solutions of the doubly nonlinear evolution j(p)((v) over circle (t)) + partial derivative Phi(v(t)) there exists 0 (a,e,t > 0) and more generally p -curves of maximal slope for Phi. We show that both schemes have the remarkable property that the Rayleigh quotient is nonincreasing along solutions and that properly scaled solutions converge to a minimizer of Phi(u)/parallel to u parallel to(p). These results are new even for Hilbert spaces and their primary application is in the approximation of optimal constants and extremal functions for inequalities in Sobolev spaces.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. Laptev, Ari PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt584",{id:"formSmash:items:resultList:13:j_idt584",widgetVar:"widget_formSmash_items_resultList_13_j_idt584",onLabel:"Laptev, Ari ",offLabel:"Laptev, Ari ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt587",{id:"formSmash:items:resultList:13:j_idt587",widgetVar:"widget_formSmash_items_resultList_13_j_idt587",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Naboko, S.Safronov, O.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Szego condition for a multidimensional Schrodinger operator2005In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 219, no 2, p. 285-305Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:13:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_13_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider spectral properties of a Schrodinger operator perturbed by a potential vanishing at infinity and prove that the corresponding spectral measure satisfies a Szego-type condition.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 15. Larson, Simon PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt584",{id:"formSmash:items:resultList:14:j_idt584",widgetVar:"widget_formSmash_items_resultList_14_j_idt584",onLabel:"Larson, Simon ",offLabel:"Larson, Simon ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A bound for the perimeter of inner parallel bodies2016In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 271, no 3, p. 610-619Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:14:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_14_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the original body and states that. |∂Ωt|≥(1-tr)+n-1|∂Ω|. In particular the bound is independent of any regularity properties of ∂Ω. As a by-product of the proof we establish precise conditions for equality. The proof, which is straightforward, is based on the construction of an extremal set for a certain optimization problem and the use of basic properties of mixed volumes.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. Shimorin, Serguei PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt584",{id:"formSmash:items:resultList:15:j_idt584",widgetVar:"widget_formSmash_items_resultList_15_j_idt584",onLabel:"Shimorin, Serguei ",offLabel:"Shimorin, Serguei ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Commutant lifting and factorization of reproducing kernels2005In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 224, no 1, p. 134-159Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:15:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_15_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A general version of the commutant lifting theorem for operators between different spaces is proved. It includes as special cases the lifting theorems of Ball-Trent-Vinnikov and Volberg-Treil. A multivariable variant of the Volberg-Treil theorem is obtained as a corollary. A certain factorization property of reproducing kernels is shown to be a sufficient condition for the lifting. Another factorization property is shown to be a necessary condition.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 17. Shimorin, Serguei PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Complete Nevanlinna-Pick property of Dirichlet-type spaces2002In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 191, no 2, p. 276-296Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:16:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_16_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We prove that all Dirichlet-type spaces of functions analytic in the unit disk whose derivatives are square area integrable with superharmonic weights have complete Nevanlinna-Pick reproducing kernels. As a corollary, we obtain a commutant lifting theorem for cyclic analytic two-isometries.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. Wennman, Aron PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt584",{id:"formSmash:items:resultList:17:j_idt584",widgetVar:"widget_formSmash_items_resultList_17_j_idt584",onLabel:"Wennman, Aron ",offLabel:"Wennman, Aron ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Discrepancy densities for planar and hyperbolic zero packing2017In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 272, no 12, p. 5282-5306Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:17:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_17_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the problem of geometric zero packing, recently introduced by Hedenmalm [7]. There are two natural densities associated with this problem: the discrepancy density ρH, given by ρH=liminfr→1−inff∫D(0,r)((1−|z|2)|f(z)|−1)2dA(z)1−|z|2∫D(0,r)dA(z)1−|z|2 which measures the discrepancy in optimal approximation of (1−|z|2)−1 with the modulus of polynomials f, and its relative, the tight discrepancy density ρH ⁎, which will trivially satisfy ρH≤ρH ⁎. These densities have deep connections to the boundary behaviour of conformal mappings with k-quasiconformal extensions, which can be seen from Hedenmalm's result that the universal asymptotic variance Σ2 is related to ρH ⁎ by Σ2=1−ρH ⁎. Here we prove that in fact ρH=ρH ⁎, resolving a conjecture by Hedenmalm in the positive. The natural planar analogues ρC and ρC ⁎ to these densities make contact with work of Abrikosov on Bose–Einstein condensates. As a second result we prove that also ρC=ρC ⁎. The methods are based on Ameur, Hedenmalm and Makarov's Hörmander-type ∂¯-estimates with polynomial growth control [2]. As a consequence we obtain sufficiency results on the degrees of approximately optimal polynomials.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:17:j_idt622:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 19. Wennman, Aron PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt584",{id:"formSmash:items:resultList:18:j_idt584",widgetVar:"widget_formSmash_items_resultList_18_j_idt584",onLabel:"Wennman, Aron ",offLabel:"Wennman, Aron ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Discrepancy densities for planar and hyperbolic zero packing2017In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 272, no 12, p. 5282-5306Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt622_0_j_idt623",{id:"formSmash:items:resultList:18:j_idt622:0:j_idt623",widgetVar:"widget_formSmash_items_resultList_18_j_idt622_0_j_idt623",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the problem of geometric zero packing, recently introduced by Hedenmalrn [7]. There are two natural densities associated with this problem: the discrepancy density pa, given by rho(H) = lim (r -> 1-) inf inf(f) integral(D(0,r)) ((1 - vertical bar z vertical bar(2)) vertical bar f(z)vertical bar - 1)(2) dA(z)/1 - vertical bar z vertical bar(2)/ integral(D(0,r)) dA(z)/1 - vertical bar z vertical bar(2) which measures the discrepancy in optimal approximation of (1 - vertical bar z vertical bar(2))(-1) with the modulus of polynomials f, and its relative, the tight discrepancy density rho*(H), which will trivially satisfy pH < per. These densities have deep connections to the boundary behaviour of conformal mappings with k-quasiconformal extensions, which can be seen from Hedenmalm's result that the universal asymptotic variance Sigma(2) is related to rho(H)* by Sigma(2) = 1 - rho(H)* . Here we prove that in fact rho(H) = rho(H)*, resolving a conjecture by Hedenmalm in the positive. The natural planar analogues rho(C) and rho(C)* to these densities make contact with work of Abrikosov on Bose Einstein condensates. As a second result we prove that also rho(C) = rho(C)*. The methods are based on Ameur, Hedenmalm and Makarov's Hormander-type <(partial derivative)over bar>-estimates with polynomial growth control [2]. As a consequence we obtain sufficiency results on the degrees of approximately optimal polynomials.

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