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  • 1. Ammann, B.
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, E.
    The conformal Yamabe constant of product manifolds2013In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 141, no 1, p. 295-307Article in journal (Refereed)
    Abstract [en]

    Let (V, g) and (W, h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V × W, g + h) in terms of the conformal Yamabe constants of (V, g) and (W, h).

  • 2.
    Bjorklund, Michael
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Fish, Alexander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Equidistribution of dilations of polynomial curves in nilmanifolds2009In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 137, no 6, p. 2111-2123Article in journal (Refereed)
    Abstract [en]

    In this paper we study the asymptotic behaviour under dilations of probability measures supported on polynomial curves in nilmanifolds. We prove, under some mild conditions, the effective equidistribution of such measures to the Haar measure. We also formulate a mean ergodic theorem for R-n-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necessary dilation of a given smooth curve in R-n so that the canonical projection onto T-n is epsilon-dense.

  • 3.
    Björner, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Vorwerk, Kathrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the connectivity of manifold graphs2015In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 10, p. 4123-4132Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following way: The graph of a d-dimensional simplicial compact manifold M is (2d - b_M)-connected. The parameter b_M has the property that b_M = 0 if the complex M is flag. Hence, our result interpolates between Barnette's theorem (1982) that all d-manifold graphs are (d+1)-connected and Athanasiadis' theorem (2011) that flag d-manifold graphs are 2d-connected. The definition of b_M involves the concept of banner triangulations of manifolds, a generalization of flag triangulations.

  • 4.
    Boij, Mats
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Carlini, Enrico
    Geramita, Anthony V.
    Monomials as sums of powers: The real binary case2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 9, p. 3039-3043Article in journal (Refereed)
    Abstract [en]

    We generalize an example, due to Sylvester, and prove that any monomial of degree d in R[x(0), x(1)], which is not a power of a variable, cannot be written as a linear combination of fewer than d powers of linear forms.

  • 5.
    Boij, Mats
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Zanello, Fabrizio
    Level algebras with bad properties2007In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 9, p. 2713-2722Article in journal (Refereed)
    Abstract [en]

    This paper can be seen as a continuation of the works contained in the recent article (J. Alg., 305 (2006), 949-956) of the second author, and those of Juan Migliore (math. AC/0508067). Our results are: 1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property ( WLP). In fact, for e >> 0, we will construct a codimension three, type two h- vector of socle degree e such that all the level algebras with that h-vector do not have the WLP. We will also describe the family of those algebras and compute its dimension, for each e >> 0. 2). There exist reduced level sets of points in P-3 of type two whose artinian reductions all fail to have theWLP. Indeed, the examples constructed here have the same h- vectors we mentioned in 1). 3). For any integer r >= 3, there exist non- unimodal monomial artinian level algebras of codimension r. As an immediate consequence of this result, we obtain another proof of the fact (first shown by Migliore in the abovementioned preprint, Theorem 4.3) that, for any r >= 3, there exist reduced level sets of points in P-r whose artinian reductions are non- unimodal.

  • 6.
    Brändén, Petter
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Chasse, Matthew
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Infinite log-concavity for polynomial pólya frequency sequences2015In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 12, p. 5147-5158Article in journal (Refereed)
    Abstract [en]

    McNamara and Sagan conjectured that if a0, a1, a2, . . . is a Pólya frequency (PF) sequence, then so is (formula presented), . . .. We prove this conjecture for a natural class of PF-sequences which are interpolated by polynomials. In particular, this proves that the columns of Pascal’s triangle are infinitely log-concave, as conjectured by McNamara and Sagan. We also give counterexamples to the first mentioned conjecture. Our methods provide families of nonlinear operators that preserve the property of having only real and nonpositive zeros.

  • 7.
    Brändén, Petter
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Krasikov, Ilia
    Shapiro, Boris
    ELEMENTS OF POLYA-SCHUR THEORY IN THE FINITE DIFFERENCE SETTING2016In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 11, p. 4831-4843Article in journal (Refereed)
    Abstract [en]

    The Polya-Schur theory describes the class of hyperbolicity preservers, i.e., the class of linear operators acting on univariate polynomials and preserving real-rootedness. We attempt to develop an analog of Polya-Schur theory in the setting of linear finite difference operators. We study the class of linear finite difference operators preserving the set of real-rooted polynomials whose mesh (i.e., the minimal distance between the roots) is at least one. In particular, we prove a finite difference version of the classical Hermite-Poulain theorem and several results about discrete multiplier sequences.

  • 8. Byrnes, Christopher I.
    et al.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A note on the Jacobian conjecture2008In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 9, p. 3007-3011Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the Jacobian conjecture for a map f of complex a. ne spaces of dimension n. It is well known that if f is proper, then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if f is proper onto its image.

  • 9. Bär, C.
    et al.
    Dahl, Mattias
    KTH, Superseded Departments, Mathematics.
    The first Dirac eigenvalues on manifolds with positive scalar curvature2004In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 11, p. 3337-3344Article in journal (Refereed)
    Abstract [en]

    We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.

  • 10. Cavalieri, Renzo
    et al.
    Yang, Stephanie
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Tautological pairings on moduli spaces of curves2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 1, p. 51-62Article in journal (Refereed)
    Abstract [en]

    We discuss analogs of Faber's conjecture for two nested sequences of partial compactifications of the moduli space of smooth pointed curves. We show that their tautological rings are one-dimensional in top degree but sometimes do not satisfy Poincare duality.

  • 11.
    Chacholski, Wojciech
    et al.
    KTH, Superseded Departments, Mathematics.
    Parent, Paul-Eugene
    KTH, Superseded Departments, Mathematics.
    Stanley, D.
    Cellular generators2004In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 11, p. 3397-3409Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is twofold. On the one hand, we show that the kernelof the Bousfield periodization functor P-A is cellularly generated by a space B, i.e., we construct a space B such that the smallest closed class C( B) containing B is exactly C( A). On the other hand, we show that the partial order (Spaces, much greater than) is a complete lattice, where B much greater than A if B is an element of C(A). Finally, as a corollary we obtain Bousfield's theorem, which states that (Spaces, >) is a complete lattice, where B > A if B is an element of.

  • 12. Claesson, Anders
    et al.
    Linusson, Svante
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    n! MATCHINGS, n! POSETS2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 2, p. 435-449Article in journal (Refereed)
    Abstract [en]

    We show that there are n! matchings on 2n points without so-called left (neighbor) nestings. We also define a set of naturally labeled (2 + 2)-free posets and show that there are n! such posets on 71 elements. Our work was inspired by Bousquet-Melou, Claesson, Dukes and Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884-909]. They gave bijections between four classes of combinatorial objects: matchings with no neighbor nestings (due to Stoimenow), unlabeled (2 + 2)-free posets, permutations avoiding a specific pattern, and so-called ascent sequences. We believe that certain statistics on our matchings and posets could generalize the work of Bousquet-Melou et al., and we make a conjecture to that effect. We also identify natural subsets of matchings and posets that are equinumerous to the class of unlabeled (2 + 2)-free posets. We give bijections that show the equivalence of (neighbor) restrictions on nesting arcs with (neighbor) restrictions on crossing arcs. These bijections are thought to be of independent interest. One of the bijections factors through certain upper-triangular integer matrices that have recently been studied by Dukes and Parviainen [Electron. J. Combin. 17 (2010) #R53].

  • 13.
    De Stefani, Alessandro
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Polstra, Thomas
    Yao, Yongwei
    GENERALIZING SERRE'S SPLITTING THEOREM AND BASS'S CANCELLATION THEOREM VIA FREE-BASIC ELEMENTS2018In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 4, p. 1417-1430Article in journal (Refereed)
    Abstract [en]

    We give new proofs of two results of Stafford, which generalize two famous Theorems of Serre and Bass regarding projective modules. Our techniques are inspired by the theory of basic elements. Using these methods we further generalize Serre's Splitting Theorem by imposing a condition to the splitting maps, which has an application to the case of Cartier algebras.

  • 14.
    Di Rocco, Sandra
    et al.
    KTH, Superseded Departments, Mathematics.
    Sommese, A. J.
    Line bundles for which a projectivized jet bundle is a product2001In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 129, no 6, p. 1659-1663Article in journal (Refereed)
    Abstract [en]

    We characterize the triples (X, L, H), consisting of line bundles L and H on a complex projective manifold X, such that for some positive integer k, the k-th holomorphic jet bundle of L, J(k) (X, L), is isomorphic to a direct sum H + . . . + H.

  • 15.
    Frank, Rupert L.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Princeton University, United States.
    Laptev, Ari
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Imperial College London, United Kingdom.
    Molchanov, Stanislav
    Eigenvalue estimates for magnetic Schrödinger operators in domains2008In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 12, p. 4245-4255Article in journal (Refereed)
    Abstract [en]

    Inequalities are derived for sums and quotients of eigenvalues of magnetic Schrodinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.

  • 16.
    Gustafsson, Björn
    et al.
    KTH, Superseded Departments, Mathematics.
    Prokhorov, D.
    Vasil'ev, A.
    Infinite lifetime for the starlike dynamics in Hele-Shaw cells2004In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 9, p. 2661-2669Article in journal (Refereed)
    Abstract [en]

    One of the folklore questions in the theory of free boundary problems is the lifetime of the starlike dynamics in a Hele-Shaw cell. We prove precisely that, starting with a starlike analytic phase domain Omega(0), the Hele-Shaw chain of subordinating domains Omega( t), Omega(0) = Omega(0), exists for an infinite time under injection at the point of starlikeness.

  • 17.
    Gustafsson, Björn
    et al.
    KTH, Superseded Departments, Mathematics.
    Putinar, M.
    On exact quadrature formulas for harmonic functions on polyhedra2000In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 128, no 5, p. 1427-1432Article in journal (Refereed)
    Abstract [en]

    A classical quadrature result for analytic functions of a complex variable due to Motzkin and Schoenberg is extended to higher dimensions. A general scheme for integrating on polyhedra solutions of partial differential equations is discussed.

  • 18.
    Hedenmalm, Håkan
    KTH, Superseded Departments, Mathematics.
    Thin interpolating sequences and three algebras of bounded functions1987In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 99, p. 489-495Article in journal (Refereed)
  • 19.
    Hedenmalm, Håkan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Kayumov, Ilgiz
    On the Makarov law of the iterated logarithm2007In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 7, p. 2235-2248Article in journal (Refereed)
    Abstract [en]

    We obtain considerable improvement of Makarov's estimate of the boundary behavior of a general conformal mapping from the unit disk to a simply connected domain in the complex plane. We apply the result to improve Makarov's comparison of harmonic measure with Hausdorff measure on simply connected domains.

  • 20.
    Hedenmalm, Håkan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Shimorin, Serguei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the universal integral means spectrum of conformal mappings near the origin2007In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 7, p. 2249-2255Article in journal (Refereed)
    Abstract [en]

    We improve the local estimate near the origin of the integral means spectrum for conformal mappings obtained in our paper from 2005. We also study some algebraic aspects of higher order forms associated with the given conformal mapping.

  • 21.
    Hekmati, Pedram
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Integrability Criterion for Abelian Extensions of Lie Groups2010In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 11, p. 4137-4148Article in journal (Refereed)
    Abstract [en]

    We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras (g) over cap = g circle plus(omega) a integrates to a corresponding Lie group extension A (sic) (G) over cap (sic) G, where G is connected, simply connected and A congruent to a/Gamma for some discrete subgroup Gamma subset of a. When pi(1) (G) not equal 0, the kernel A is replaced by a central extension (A) over cap of pi(1) (G) by A.

  • 22. Hynd, Ryan
    et al.
    Lindgren, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    INVERSE ITERATION FOR p-GROUND STATES2016In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 5, p. 2121-2131Article in journal (Refereed)
    Abstract [en]

    We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for p is an element of (1, infinity) and a given domain Omega subset of R-n, we analyze a scheme that allows us to approximate the smallest value the ratio integral(Omega)vertical bar D psi vertical bar(p)dx/ integral(Omega)vertical bar psi vertical bar(p)dx can assume for functions psi that vanish on partial derivative Omega. The scheme in question also provides a natural way to approximate minimizing psi. Our analysis also extends in the limit as p -> infinity and thereby fashions a new approximation method for ground states of the infinity Laplacian.

  • 23.
    Laksov, Dan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On zanello's lower bound for level algebras2013In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 141, no 5, p. 1519-1527Article in journal (Refereed)
    Abstract [en]

    We consider the proof of Söderberg of Zanello's lower bound for the Hilbert function of level algebras from the point of view of vector spaces. Our results, when specialised to level algebras, generalise those of Zanello and Söderberg to the case when the modules involved may have nontrivial annihilators. In the process we clarify why the methods of Zanello and Söderberg consist of two distinct parts. As a contrast we show that for polynomial rings, Zanello's bound, in the generic case, can be obtained by simple manipulations of numbers without dividing into two separate cases. We also consider the inclusion-exclusion principle of dimensions of vector spaces used by Zanello in special cases. It turns out that the resulting alternating sums are extremely difficult to handle and have many unexpected properties. This we illustrate by a couple of results and examples. The examples show that the inclusion-exclusion principle does not hold for vector spaces in the way it is used by Zanello.

  • 24.
    Larson, Simon
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the remainder term of the Berezin inequality on a convex domain2017In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 145, no 5, p. 2167-2181Article in journal (Refereed)
    Abstract [en]

    We study the Dirichlet eigenvalues of the Laplacian on a convex domain in R-n, with n >= 2. In particular, we generalize and improve upper bounds for the Riesz means of order sigma >= 3/2 established in an article by Geisinger, Laptev and Weidl. This is achieved by refining estimates for a negative second term in the Berezin inequality. The obtained remainder term reflects the correct order of growth in the semi-classical limit and depends only on the measure of the boundary of the domain. We emphasize that such an improvement is for general Omega subset of R-n not possible and was previously known to hold only for planar convex domains satisfying certain geometric conditions. As a corollary we obtain lower bounds for the individual eigenvalues lambda(k), which for a certain range of k improves the Li-Yau inequality for convex domains. However, for convex domains one can use different methods to obtain even stronger lower bounds for lambda(k)

  • 25.
    Lester, Stephen
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Tel Aviv University, Israel.
    On the variance of sums of divisor functions in short intervals2016In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 12, p. 5015-5027Article in journal (Refereed)
    Abstract [en]

    Given a positive integer n the k-fold divisor function dk(n) equals the number of ordered k-tuples of positive integers whose product equals n. In this article we study the variance of sums of d(k)(n) in short intervals and establish asymptotic formulas for the variance of sums of d(k)(n) in short intervals of certain lengths for k = 3 and for k >= 4 under the assumption of the Lindelof hypothesis.

  • 26.
    Lindgren, Erik
    Department of Mathematical Sciences, Norwegian University of Science and Technology, Alfred Getz vei 1, NO-7491 Trondheim, Norway .
    On the regularity of solutions of the inhomogeneous infinity laplace equation2014In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 142, no 1, p. 277-288Article in journal (Refereed)
    Abstract [en]

    We study the inhomogeneous infinity Laplace equation and prove that for bounded and continuous inhomogeneities, any blow-up is linear but not necessarily unique. If, in addition, the inhomogeneity is assumed to be C-1, then we prove that any solution is differentiable, i.e., that any blow-up is unique.

  • 27.
    Maakestad, Helge
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A note on principal parts on projective space and linear representations2005In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 133, no 2, p. 349-355Article in journal (Refereed)
    Abstract [en]

    Let H be a closed subgroup of a linear algebraic group G defined over a field of characteristic zero. There is an equivalence of categories between the category of linear finite-dimensional representations of H, and the category of finite rank G-homogeneous vector bundles on G/H. In this paper we will study this correspondence for the sheaves of principal parts on projective space, and we describe the representation corresponding to the principal parts of a line bundle on projective space.

  • 28.
    McCormick, Stephen
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On a minkowski-like inequality for asymptotically flat static manifolds2018In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 9, p. 4039-4046Article in journal (Refereed)
    Abstract [en]

    The Minkowski inequality is a classical inequality in differential geometry giving a bound from below on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than ℝn; for example, such an inequality holds for surfaces in spatial Schwarzschild and AdS-Schwarzschild manifolds. In this note, we adapt a recent analysis of Y. Wei to prove a Minkowski-like inequality for general static asymptotically flat manifolds.

  • 29.
    Miles, Richard
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Ward, Thomas
    Orbit-counting for nilpotent group shifts2009In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 137, no 4, p. 1499-1507Article in journal (Refereed)
    Abstract [en]

    We study the asymptotic behaviour of the orbit-counting function and a dynamical Mertens' theorem for the full G-shift for a. nitely-generated torsion-free nilpotent group G. Using bounds for the Mobius function on the lattice of subgroups of finite index and known subgroup growth estimates, we find a single asymptotic of the shape Sigma vertical bar(tau vertical bar <= N)1/e(h)vertical bar tau vertical bar similar to C N-alpha(log N)(beta) where vertical bar tau vertical bar is the cardinality of the finite orbit tau and h denotes the topological entropy. For the usual orbit- counting function we find upper and lower bounds, together with numerical evidence to suggest that for actions of noncyclic groups there is no single asymptotic in terms of elementary functions.

  • 30.
    Miles, Richard
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ward, Thomas
    Uniform periodic point growth in entropy rank one2008In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 1, p. 359-365Article in journal (Refereed)
    Abstract [en]

    We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.

  • 31.
    Shimorin, Serguei
    KTH, Superseded Departments, Mathematics.
    On Beurling-type theorems in weighted l(2) and Bergman spaces2003In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 131, no 6, p. 1777-1787Article in journal (Refereed)
    Abstract [en]

    We prove that analytic operators satisfying certain series of operator inequalities possess the wandering subspace property. As a corollary, we obtain Beurling-type theorems for invariant subspaces in certain weighted l(2) and Bergman spaces.

  • 32.
    Sjölin, Per
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Some remarks on singular oscillatory integrals and convolution operators2017In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 145, no 9, p. 3843-3848Article in journal (Refereed)
    Abstract [en]

    In this note we study the relation between oscillatory integral operators and convolution operators, and also the sharpness of L-p-estimates for singular oscillatory integral operators.

  • 33.
    Sjöstrand, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Expected length of a product of random reflections2012In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, no 12, p. 4369-4380Article in journal (Refereed)
    Abstract [en]

    We present a simple formula for the expected number of inversions in a permutation of size n obtained by applying t random (not necessarily adjacent) transpositions to the identity permutation. More generally, for any finite irreducible Coxeter group belonging to one of the infinite families (type A, B, D, and I), an exact expression is obtained for the expected length of a product of t random reflections.

  • 34.
    Söderberg, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On Zanello's lower bound for generic quotients of level algebras2014In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 142, no 12, p. 4025-4028Article in journal (Refereed)
    Abstract [en]

    We give a shorter and more straightforward proof of a theorem of Zanello on lower bounds for Hilbert functions of generic level quotients of artinian level algebras.

  • 35.
    Tkachev, Vladimir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A generalization of Cartan's theorem on isoparametric cubics2010In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 8, p. 2889-2895Article in journal (Refereed)
    Abstract [en]

    We generalize the well-known result of E. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation vertical bar del f vertical bar(2)= 9 vertical bar x vertical bar(4) must be rotationally equivalent to either x(n)(3) - 3x(n) (x(1)(2) + ... + x(n-1)(2)) or to one of four exceptional Cartan cubic polynomials in dimensions n = 5,8,14,26.

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