The Khavinson-Shapiro conjecture and the Bergman projection in one and several complex variables

DOI10.1007/s40315-015-0135-xzbMath1355.32006arXiv1504.04635OpenAlexW1494459490WikidataQ123238226 ScholiaQ123238226MaRDI QIDQ291931

Alan R. Legg

Publication date: 10 June 2016

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.04635

zbMATH Keywords

Dirichlet problemBergman spaceellipsoid

Mathematics Subject Classification ID

Boundary behavior of harmonic functions in higher dimensions (31B25) Bergman spaces of functions in several complex variables (32A36) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (2)

Unnamed Item ⋮ Ellipses and polynomial-to-polynomial mapping of weighted Szegő projections

Cites Work

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• Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
• The Khavinson-Shapiro conjecture and polynomial decompositions
• Unique continuation theorems for the \(\bar \partial\)-operator and applications
• Proper holomorphic mappings between circular domains
• Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions
• The Dirichlet Problem for Ellipsoids
• A Tale of Ellipsoids in Potential Theory
• An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat Problem
• Dirichlet's Problem When the Data is an Entire Function
• Polynomial solutions to Dirichlet problems
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)

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