The Khavinson-Shapiro conjecture and polynomial decompositions

DOI10.1016/j.jmaa.2010.09.069zbMath1223.35101OpenAlexW2058812366WikidataQ123245897 ScholiaQ123245897MaRDI QIDQ624608

Hermann Render, Erik Lundberg

Publication date: 9 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.09.069

zbMATH Keywords

Dirichlet problempolynomial solvabilityFischer decompositionpolyharmonic polynomialspolynomial dataspecial geometries

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Polynomials in number theory (11C08) Solutions to PDEs in closed form (35C05)

Related Items (10)

The Khavinson-Shapiro conjecture and the Bergman projection in one and several complex variables ⋮ A characterization of the Khavinson-Shapiro conjecture via Fischer operators ⋮ Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations ⋮ Approximating \overline{𝑧} in the Bergman Space ⋮ On polyharmonic polynomials ⋮ Ellipses and polynomial-to-polynomial mapping of weighted Szegő projections ⋮ A Fischer type decomposition theorem from the apolar inner product ⋮ The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces ⋮ Harmonic Functions in Slabs and Half-Spaces ⋮ Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Cites Work

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