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  • 1.
    Aleksanyan, Hayk
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). The University of Edinburgh.
    Shahgholian, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Sjölin, Per
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    L2-estimates for singular oscillatory integral operators2016Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 441, nr 2, s. 529-548Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L2L2 type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in R3.

  • 2.
    Ameur, Yacin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Cwikel, Michael
    Technion Israel Inst Technol, Dept Math.
    On the K-divisibility constant for some special finite-dimensional Banach couples2009Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 360, nr 1, s. 130-155Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove new estimates of the K-divisibility constants for some special Banach couples. In particular, we prove that the K-divisibility constant for a couple of the form (U circle plus V, U) where U and V are non-trivial Hilbert spaces equals 2/root 3. We also prove estimates for the K-divisibility constant of the two-dimensional version of the couple (L-2, L-infinity), proving in particular that this couple is not exactly K-divisible. There are also several auxiliary results, including some estimates for relative Calderon constants for finite-dimensional couples.

  • 3. Bahlali, K.
    et al.
    Chighoub, F.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Mezerdi, B.
    Optimality necessary conditions in singular stochastic control problems with nonsmooth data2009Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 355, nr 2, s. 479-494Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The present paper studies the stochastic maximum principle in singular optimal control, where the state is governed by a stochastic differential equation With nonsmooth coefficients, allowing both classical control and singular control. The proof of the main result is based oil the approximation of the initial problem, by a sequence of control problems with smooth coefficients. We, then apply Ekeland's variational principle for this approximating sequence of control problems, in order to establish necessary conditions satisfied by a sequence of near optimal controls. Finally, we prove the convergence of the scheme, using Krylov's inequality in the nondegenerate case and the Bouleau-Hirsch now property in the degenerate one. The adjoint process obtained is given by means of distributional derivatives of the coefficients.

  • 4.
    Djehiche, Boualem
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Hamadene, Said
    Morlais, Marie-Amehe
    Zhao, Xuzhe
    On the equality of solutions of max-min and min-max systems of variational inequalities with interconnected bilateral obstacles2017Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, nr 1, s. 148-175Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we deal with the solutions of systems of PDEs with bilateral interconnected obstacles of min-max and max-min types. These systems arise naturally in stochastic switch-in zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the values of a zero-sum switching game is studied.

  • 5.
    Djehiche, Boualem
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    N'zi, Modeste
    Owo, Jean-Marc
    Stochastic viscosity solutions for SPDEs with continuous coefficients2011Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 384, nr 1, s. 63-69Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions. (C) 2010 Elsevier Inc. All rights reserved.

  • 6.
    Ekholm, Tomas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Kovarik, Hynek
    Portmann, Fabian
    Estimates for the lowest eigenvalue of magnetic Laplacians2016Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 439, nr 1, s. 330-346Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded, open, simply connected domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant magnetic field. 

  • 7.
    Gustafsson, Björn
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Putinar, Mihai
    Analytic continuation of the exponential transform from convex cavities2007Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 328, nr 2, s. 995-1006Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The analytic continuation of the exponential transform of a domain in R-n is proved under some global geometric assumptions on the boundary. Two approximation schemes of the continued transform (one based on a Taylor series truncation, the other on a global eigenfunction expansion) are also discussed.

  • 8. Hallnaes, Martin
    et al.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    A product formula for the eigenfunctions of a quartic oscillator2015Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 426, nr 2, s. 1012-1025Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the Schrodinger operator on the real line with an even quartic potential. Our main result is a product formula of the type psi(k)(x)psi(k)(y) = integral(R) psi(k)(z)K(x,y, z)dz for its eigenfunctions psi(k). The kernel function K is given explicitly in terms of the Airy function Ai(x), and it is positive for appropriate parameter values. As an application, we obtain a particular asymptotic expansion of the eigenfunctions psi(k).

  • 9.
    Hedenmalm, Håkan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    On the asymptotic free boundary for the American put option problem2006Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 314, nr 1, s. 345-362Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price movements, this problem is fairly easy to handle for options with a short lifespan, by analyzing binomial trees. It is considerably more challenging to make the decision for American put options with long lifespan. In order to provide a satisfactory analysis, we look at the corresponding free boundary problem, and show that the free boundary-which is the curve that separates the two decisions, to exercise or not to-has an asymptotic expansion, where the coefficient of the main term is expressed as an integral in terms of the free boundary. This raises the perspective that one could use numerical simulation to approximate the integral and thus get an effective way to make correct decisions for long life options.

  • 10.
    Jönsson, Ulf T.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Martin, Clyde
    Approximation with the output of linear control systems2007Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 329, nr 2, s. 798-821Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we give a new proof that for controllable and observable linear systems every L-2[0, T] function can be approximated in the L-2[0, T] sense with an output function generated by an L-2[0, T] input function. We also give a new characterization of how continuous functions on [0, T] are uniformly approximated by an output generated by a continuous input function. The relative degree of the transfer function of the system determines those functions that can be approximated. We further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions.

  • 11.
    Lenells, Jonatan
    Lund University, Sweden.
    Infinite propagation speed of the Camassa-Holm equation2007Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 325, nr 2, s. 1468-1478Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We use the inverse scattering transform to show that a solution of the Camassa-Holm equation is identically zero whenever it vanishes on two horizontal half-lines in the x-t space. In particular, a solution that has compact support at two different times vanishes everywhere, proving that the Camassa-Holm equation has infinite propagation speed.

  • 12.
    Lenells, Jonatan
    University of Cambridge, United Kingdom .
    Periodic solitons of an equation for short capillary-gravity waves2009Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 352, nr 2, s. 964-966Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the periodic solitons of an equation for short capillary-gravity waves. Although their profiles cannot be given a description in terms of a mathematical expression in closed form, we show that they are transformed by a natural change of variables to the well-known cnoidal periodic solitons of the KdV equation.

  • 13.
    Lenells, Jonatan
    Lund University, Sweden .
    Traveling wave solutions of the Degasperis-Procesi equation2005Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 306, nr 1, s. 72-82Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We classify all weak traveling wave solutions of the Degasperis-Procesi equation. In addition to smooth and peaked solutions, the equation is shown to admit more exotic traveling waves such as cuspons, stumpons, and composite waves.

  • 14.
    Mattila, Kirsti
    KTH, Tidigare Institutioner                               , Matematik.
    Restrictions of relatively Tauberian operators2003Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 287, nr 2, s. 494-503Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For operators T with the property TX1 subset of T X which in addition satisfy a spectral condition we consider conditions under which the restriction of T to a closed invariant subspace also satisfies the same inclusion on the subspace.

  • 15.
    Mauersberger, Julian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Asymptotics to all orders of the Euler-Darboux equation in a triangle2019Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 471, nr 1-2, s. 180-196Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In Einstein's theory of relativity, the interaction of two collinearly polarized plane gravitational waves can be described by a Goursat problem for the Euler Darboux equation in a triangular domain. In this paper, using a representation of the solution in terms of Abel integrals, we give a full asymptotic expansion of the solution near the diagonal of the triangle. The expansion is related to the formation of a curvature singularity of the spacetime. In particular, our framework allows for boundary data with derivatives which are singular at the corners. This level of generality is crucial for the application to gravitational waves.

  • 16.
    Peplow, Andrew
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, MWL Marcus Wallenberg Laboratoriet.
    Chandler-Wilde, S. N.
    Existence and uniqueness of solutions for acoustic scattering over infinite obstacles2008Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 345, nr 1, s. 305-321Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper considers the solution of the boundary value problem (BVP) consisting of the Helmholtz equation in the region D with a rigid boundary condition on partial derivative D and its reformulation as a boundary integral equation (BIE), over an infinite cylindrical surface of arbitrary smooth cross-section. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution of the integral equation and the corresponding boundary value problem.

  • 17.
    Sasane, Amol
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    An abstract Nyquist criterion containing old and new results2010Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 370, nr 2, s. 703-715Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.

  • 18.
    Sjölin, Per
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Soria, Fernando
    Estimates for multiparameter maximal operators of Schrödinger type2014Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 411, nr 1, s. 129-143Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Multiparameter maximal estimates are considered for operators of Schrodinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which naturally appears with a TT* argument and discuss the behavior at the endpoints. We treat in particular the case of global integrability of the maximal operator on finite time for solutions to the linear Schrodinger equation and make some comments on an open problem.

  • 19.
    Sjölin, Per
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Convergence of sequences of Schrödinger means2020Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 483, nr 1, artikel-id 123580Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study convergence almost everywhere of sequences of Schrodinger means. We also replace sequences by uncountable sets.

  • 20.
    Önskog, Thomas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Lundström, Niklas L. P.
    Olofsson, Marcus
    Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching2019Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study viscosity solutions to a system of nonlinear degenerate parabolic partial integro-differential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variableis described by an n-dimensional Lévy process. We first establish a continuous dependence estimate for viscosity sub- and supersolutions to the system under mild regularity, growth and structural assumptions on the partial integro-differential operator and on the obstacles and terminal conditions. Using the continuous dependence estimate, we obtain the comparison principle and uniqueness of viscosity solutions as well as Lipschitz regularity in the spatial variables. Our main contribution is construction of suitable families of viscosity sub- and supersolutions which we use as “barrier functions” to prove Hölder continuity in the time variable, and, through Perron’s method, existence of a unique viscosity solution. This paper generalizes parts of the results of Biswas, Jakobsen and Karlsen (2010) [BJK10] and of Lundström, Nyström and Olofsson (2014) [LNO14, LNO14b] to hold for more general systems of equations.

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