Construction and application of Bergman-type reproducing kernels for boundary and eigenvalue problems in the plane

DOI10.1080/17476933.2011.611941zbMath1264.30035OpenAlexW2087098539MaRDI QIDQ3167676

Raúl Castillo-Pérez, Vladislav V. Kravchenko, Hugo M. Campos

Publication date: 2 November 2012

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2011.611941

zbMATH Keywords

Schrödinger equationBergman kernelreproducing kernelgeneralized analytic functionpseudoanalytic function

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20)

Related Items (8)

Bounded extremal problems in Bergman and Bergman-Vekua spaces ⋮ Modified spectral parameter power series representations for solutions of Sturm-Liouville equations and their applications ⋮ First characterization of a new method for numerically solving the Dirichlet problem of the two-dimensional electrical impedance equation ⋮ Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients ⋮ Complete families of solutions for the Dirac equation using bicomplex function theory and transmutations ⋮ Some Recent Developments in the Transmutation Operator Approach ⋮ Transmutations, \(L\)-bases and complete families of solutions of the stationary Schrödinger equation in the plane ⋮ Runge property and approximation by complete systems of solutions for strongly elliptic equations

Cites Work

• Über einen Satz von Walsh für pseudoanalytische Funktionen
• Zur Approximation pseudoanalytischer Funktionen durch Pseudopolynome
• Formal powers and power series
• An outline of the theory of pseudoanalytic functions
• Eigenvalue Characterization and Computation for the Laplacian on General 2-D Domains
• Applied Pseudoanalytic Function Theory
• Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
• On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions
• The Expansion Theorem for Sigma-Manogenic Functions

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