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  • 1. Abuzyarova, Natalia
    et al.
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Branch point area methods in conformal mapping2006In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 99, p. 177-198Article in journal (Refereed)
    Abstract [en]

    The classical estimate of Bieberbach that vertical bar a(2)vertical bar <= 2 for a given univalent function phi(z) = z + a(2)z(2) +... in the class S leads to the best possible pointwise estimates of the ratio phi''(z)/phi'(z) for phi is an element of S, first obtained by K oe be and Bieberbach. For the corresponding class E of univalent functions in the exterior disk, Goluzin found in 1943 by variational methods the corresponding best possible pointwise estimates of psi(z)/psi'(z) for psi is an element of Sigma. It was perhaps surprising that this time, the expressions involve elliptic integrals. Here, we obtain an area-type theorem which has Goluzin's pointwise estimate as a corollary. This shows that Goluzin's estimate, like the K oe be-Bieberbach estimate, is firmly rooted in area-based methods. The appearance of elliptic integrals finds a natural explanation: they arise because a certain associated covering surface of the Riemann sphere is a torus.

  • 2. Aharonov, Dov
    et al.
    Shapiro, Harold S.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Solynin, Alexander Yu.
    Minimal area problems for functions with integral representation2006In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 98, p. 83-111Article in journal (Refereed)
    Abstract [en]

    We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal area a(2)-problern for convex functions and for typically real functions. The latter gives a new solution to the minimal area a(2)-problem for the class S of normalized univalent functions in the unit disc.

  • 3.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Discrete balayage and boundary sandpile2019In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 138, no 1, p. 361-403Article in journal (Refereed)
    Abstract [en]

    We introduce a new lattice growth model, which we call the boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on Z(d) (d >= 2) onto the boundary of an (a priori) unknown domain. The latter evolves through sandpile dynamics, and has the property that the mass on the boundary is forced to stay below a prescribed threshold. Since finding the domain is part of the problem, the redistribution process is a discrete model of a free boundary problem, whose continuum limit is yet to be understood. We prove general results concerning our model. These include canonical representation of the model in terms of the smallest super-solution among a certain class of functions, uniform Lipschitz regularity of the scaled odometer function, and hence the convergence of a subsequence of the odometer and the visited sites, discrete symmetry properties, as well as directional monotonicity of the odometer function. The latter (in part) implies the Lipschitz regularity of the free boundary of the sandpile.

    As a direct application of some of the methods developed in this paper, combined with earlier results on the classical abelian sandpile, we show that the boundary of the scaling limit of an abelian sandpile is locally a Lipschitz graph.

  • 4. Aleman, A.
    et al.
    Beliaev, Dmitri
    KTH, Superseded Departments, Mathematics.
    Hedenmalm, Håkan
    KTH, Superseded Departments, Mathematics.
    Real zero polynomials and Pólya-Schur type theorems2004In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 94, p. 49-60Article in journal (Refereed)
  • 5.
    Almeida, V.
    et al.
    Univ La Laguna, Dept Anal Matemat, Campus Anchieta, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain..
    Betancor, J. J.
    Univ La Laguna, Dept Anal Matemat, Campus Anchieta, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain..
    Castro, Alejandro J.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sadarangani, K.
    Univ Las Palmas Gran Canaria, Dept Matemat, Campus Tafira Baja, Las Palmas Gran Canaria 35017, Spain..
    Riesz Transforms And Multipliers For The Bessel-Grushin Operator2016In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 128, p. 51-106Article in journal (Refereed)
    Abstract [en]

    We establish that the spectral multiplier m(G(alpha)) associated to the differential operator G alpha = -Delta x + Sigma j=1m alpha j2-1/4/xj2 - vertical bar x vertical bar 2 Delta(y) on (0, infinity)(m) x R-n, which we call the Bessel-Grushin operator, is of weak type (1, 1) provided that m is in a suitable local Sobolev space. In order to do this, we prove a suitable weighted Plancherel estimate. Also, we study L-p-boundedness properties of Riesz transforms associated to G(alpha) in the case n = 1.

  • 6. Bell, S. R.
    et al.
    Ebenfelt, P.
    Khavinson, D.
    Shapiro, Harold S.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On the classical Dirichlet problem in the plane with rational data2006In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 100, p. 157-190Article in journal (Refereed)
    Abstract [en]

    We consider the Dirichlet problem for the Laplace operator with rational data on the boundary of a planar domain. Our main results include a characterization of the disk as the only domain for which all solutions are rational and a characterization of the simply connected quadrature domains as the only ones for which all solutions are algebraic of a certain type.

  • 7.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Latvala, Visa
    Univ Eastern Finland, Finland.
    The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces2018In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 135, no 1, p. 59-83Article in journal (Refereed)
    Abstract [en]

    We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a p-Poincar, inequality, 1 amp;lt; p amp;lt; a. We apply these key tools to establish a fine version of the Kellogg property, characterize finely continuous functions by means of quasicontinuous functions, and show that capacitary measures associated with Cheeger supersolutions are supported by the fine boundary of the set.

  • 8. Borcea, Julius
    et al.
    Friedland, Shmuel
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    Parametric Poincaré-Perron theorem with applications2011In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 113, no 1, p. 197-225Article in journal (Refereed)
    Abstract [en]

    We prove a parametric generalization of the classical Poincar´e- Perron theorem on stabilizing recurrence relations where we assume that the varying coefficients of a recurrence depend on auxiliary parameters and converge uniformly in these parameters to their limiting values. As an application we study convergence of the ratios of families of functions satisfying finite recurrence relations with varying functional coefficients. For example, we explicitly describe the asymptotic ratio for two classes of biorthogonal polynomials introduced by Ismail and Masson.

  • 9.
    Brändén, Petter
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Chasse, Matthew
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Classification theorems for operators preserving zeros in a strip2017In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 132, no 1, p. 177-215Article in journal (Refereed)
    Abstract [en]

    We characterize all linear operators which preserve certain spaces of entire functions whose zeros lie in a closed strip. Necessary and sufficient conditions are obtained for the related problem with real entire functions, and some classical theorems of de Bruijn and Pólya are extended. Specifically, we reveal new differential operators which map real entire functions whose zeros lie in a strip to real entire functions whose zeros lie in a narrower strip; this is one of the properties that characterize a “strong universal factor” as defined by de Bruijn. Using elementary methods, we prove a theorem of de Bruijn and extend a theorem of de Bruijn and Ilieff which states a sufficient condition for a function to have a Fourier transform with only real zeros.

  • 10.
    Damjanović, Danijela
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Abelian actions with globally hypoelliptic leafwise Laplacian and rigidity2016In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 129, no 1, p. 139-163Article in journal (Refereed)
    Abstract [en]

    In this paper, we prove several results concerning smooth Rk actions on a smooth compact manifold with the property that their leafwise Laplacian is globally hypoelliptic. Such actions are necessarily uniquely ergodic and minimal, and their cohomology is often finite dimensional, even trivial. Further, we consider a class of examples of R2 actions on two-step nilmanifolds that have globally hypoelliptic leafwise Laplacian, and we show transversal local rigidity under certain Diophantine conditions.

  • 11.
    Gardiner, Stephen J
    et al.
    University of College Dublin.
    Sjödin, Tomas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Two-phase quadrature domains2012In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 116, p. 335-354Article in journal (Refereed)
    Abstract [en]

    Recent work on two-phase free boundary problems has led to the investigation of a new type of quadrature domain for harmonic functions. This paper develops a method of constructing such quadrature domains based on the technique of partial balayage, which has proved to be a useful tool in the study of one-phase quadrature domains and Hele-Shaw flows.

  • 12.
    Getsadze, Rostom
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    On Cesàro summability of Fourier series with respect to double complete orthogonal systems 2007In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 102, p. 209-223Article in journal (Refereed)
  • 13. Gröchenig, Karl-Heinz
    et al.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces2011In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 114, no 1, p. 255-283Article in journal (Refereed)
    Abstract [en]

    We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function \omega and suitable window function \varphi, the Toeplitz operator (or localization operator) TP _\varphi (\omega ) is an isomorphism from M^{p,q}_{(\omega _0)} into M^{p,q}_{(\omega _0/\omega )} for every p,q\in [1,\infty ] and arbitrary weight function \omega _0. The methods involve the pseudo-differential calculus of Bony and Chemin and the Wiener algebra property of certain symbol classes of pseudo-di®erential operators.

  • 14.
    Hedenmalm, Håkan
    KTH, Superseded Departments, Mathematics.
    Bounded analytic functions and closed ideals1987In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 48, p. 142-166Article in journal (Refereed)
  • 15.
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Heisenberg's uncertainty principle in the sense of Beurling2012In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 118, no 2, p. 691-702Article in journal (Refereed)
    Abstract [en]

    We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering a fundamentally different proof which allows us to weaken the assumptions rather substantially. The new formulation is pretty much optimal, as can be seen from examples. Our arguments involve Fourier and Mellin transforms. We also introduce a version which applies to two given functions. Finally, we show how our approach applies in the higher dimensional setting.

  • 16.
    Hedenmalm, Håkan
    KTH, Superseded Departments, Mathematics.
    The dual of a Bergman space on simply connected domains2002In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 88, p. 311-335Article in journal (Refereed)
  • 17.
    Jaye, B.J.
    et al.
    Department of Mathematics, University of Missouri, Columbia, MO, 65211, United States, Department of Mathematics, Kent State University, Kent, OH, 44240, United States.
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Verbitsky, I.E.
    Department of Mathematics, University of Missouri, Columbia, MO, 65211, United States.
    Existence and regularity of positive solutions of elliptic equations of Schrödinger type2012In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 118, no 2, p. 577-621Article in journal (Refereed)
    Abstract [en]

    We prove the existence of positive solutions with optimal local regularity of the homogeneous equation of Schrödinger type, for an arbitrary open Ω ⊆ ℝn under only a form-boundedness assumption on σ ∈ D′(Ω) and ellipticity assumption on A ∈ L∞(Ω)n×n. We demonstrate that there is a two-way correspondence between form boundedness and existence of positive solutions of this equation as well as weak solutions of the equation with quadratic nonlinearity in the gradient, As a consequence, we obtain necessary and sufficient conditions for both formboundedness (with a sharp upper form bound) and positivity of the quadratic form of the Schrödinger type operator H = -div(A∇·)-σ with arbitrary distributional potential σ ∈ D′(Ω), and give examples clarifying the relationship between these two properties. © 2012 Hebrew University Magnes Press.

  • 18.
    Kresin, Gershon
    et al.
    Ariel Univ, Israel.
    Mazya, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. Univ Liverpool, England; RUDN Univ, Russia.
    Invariant convex bodies for strongly elliptic systems2018In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 135, no 1, p. 203-224Article in journal (Refereed)
    Abstract [en]

    We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies are obtained for linear systems without zero order term on bounded domains and quasilinear systems of special form on bounded domains and on a class of unbounded domains. These conditions are formulated in algebraic form. They describe relation between the geometry of the invariant convex body and the coefficients of the system. Next, necessary conditions, which are also sufficient, for the invariance of some convex bodies are found for elliptic homogeneous systems with constant coefficients in a half-space. The necessary conditions are derived by using a criterion on the invariance of convex bodies for normalized matrix-valued integral transforms also obtained in the paper. In contrast with the previous studies of invariant sets for elliptic systems, no a priori restrictions on the coefficient matrices are imposed.

  • 19.
    Kurasov, Pavel
    Stockholm University, Faculty of Science, Department of Mathematics.
    Triplet extensions I: Semibounded operators in the scale of Hilbert spaces2009In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 107, p. 251-286Article in journal (Refereed)
    Abstract [en]

    The extension theory for semibounded symmetric operators is generalized by including operators acting in a triplet of Hilbert spaces. We concentrate our attention on the case where the minimal operator is essentially self-adjoint in the basic Hilbert space and construct a family of its self-adjoint extensions inside the triplet. All such extensions can be described by certain boundary conditions, and a natural counterpart of Krein's resolvent formula is obtained.

  • 20.
    Lindgren, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lindqvist, P.
    Regularity of the p-Poisson equation in the plane2017In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 132, no 1, p. 217-228Article in journal (Refereed)
    Abstract [en]

    We study the regularity of the p-Poisson equation Δpu=h, h∈Lq, in the plane. In the case p &gt; 2 and 2 &lt; q &lt; ∞, we obtain the sharp Hölder exponent for the gradient. In the other cases, we come arbitrarily close to the sharp exponent.

  • 21. Pasechnik, Dmitrii V.
    et al.
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    On polygonal measures with vanishing harmonic moments2014In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 123, p. 281-301Article in journal (Refereed)
    Abstract [en]

    A polygonal measure is the sum of finitely many real constant density measures supported on triangles in a,. Given a finite set S aS, a,, we study the existence of polygonal measures spanned by triangles with vertices in S, all of whose harmonic moments vanish. We show that for generic S, the dimension of the linear space of such measures is . We also investigate the situation in which the density for such measure takes on only values 0 or +/- 1. This corresponds to pairs of polygons of unit density having the same logarithmic potential at a. We show that such (signed) measures do not exist for |S| a parts per thousand currency sign 5, but that for each n a parts per thousand yen 6 one can construct an S, with |S| = n, giving rise to such a measure.

  • 22.
    Pelander, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Solvability of differential equations on open subsets of the Sierpinski gasket2007In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 102, no 1, p. 359-369Article in journal (Refereed)
    Abstract [en]

    We give necessary and sufficient conditions on the polynomial p for the differential equation p(Delta)u = f, based on the Laplacian, to be solvable on any open subset of the Sierpinski gasket for any f continuous on that subset. For general p, we find the open subsets on which p(Delta)u = f is solvable for any continuous f.

  • 23.
    Radnell, David
    et al.
    Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
    Schippers, Eric
    Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials2017In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 132, no 1, p. 229-245Article in journal (Refereed)
    Abstract [en]

    Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1 . Consider quasiconformal maps f : Σ → Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t,·) : Σ → Σ1 is independent of t on the boundary curves; that is H(t,p) = f(p) for all p ∈ ∂Σ.

  • 24. Staubach, Wolfgang
    Wiener path integrals and the fundamental solution for the Heisenberg Laplacian2003In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 91, p. 389-400Article in journal (Refereed)
1 - 24 of 24
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