On polyharmonic polynomials

DOI10.1007/s10474-023-01323-9arXiv2204.05430OpenAlexW4367842256MaRDI QIDQ6097387

Sławomir Michalik, Hubert Grzebuła

Publication date: 5 June 2023

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.05430

zbMATH Keywords

homogeneous polynomialorthogonal projectionpolyharmonic polynomial

Mathematics Subject Classification ID

Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Cites Work

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• A characterization of the Khavinson-Shapiro conjecture via Fischer operators
• Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
• The Khavinson-Shapiro conjecture and polynomial decompositions
• On the mean value property for polyharmonic functions
• A Dirichlet type problem for complex polyharmonic functions
• Summable solutions of some partial differential equations and generalised integral means
• Polyharmonic cardinal splines
• Reproducing kernels for polyharmonic polynomials
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Pythagorean identity for polyharmonic polynomials
• Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions
• Harmonic Function Theory
• An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat Problem
• Radial Basis Functions
• Spherical polyharmonics and Poisson kernels for polyharmonic functions
• Harmonic Polynomials and Dirichlet-Type Problems

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