Harmonic Polynomials and Dirichlet-Type Problems

DOI10.2307/2161905zbMath0848.31002OpenAlexW4236276759MaRDI QIDQ4874274

Sheldon Axler, Wade C. Ramey

Publication date: 21 April 1996

Full work available at URL: https://doi.org/10.2307/2161905

zbMATH Keywords

Dirichlet problemNeumann problemBergman projection problembiDirichlet problemPoisson integral of a polynomial

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (15)

Harmonic polynomial decompositions over commutative Q-algebras ⋮ Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations ⋮ On polyharmonic polynomials ⋮ Harmonic Hierarchies for Polynomial Optimization ⋮ The harmonic transvector algebra in two vector variables ⋮ An explicit solution to the Dirichlet problem with rational holomorphic data in terms of a Riemann mapping ⋮ Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions ⋮ Homogeneous Partial Derivatives of Radial Functions ⋮ On the solution of the Dirichlet problem with rational holomorphic boundary data ⋮ The Neumann problem on ellipsoids ⋮ The Dirichlet problem on quadratic surfaces ⋮ Rotational symmetries in polynomial rings ⋮ Compact Hankel operators on weighted harmonic Bergman spaces ⋮ Fischer decompositions for entire functions and the Dirichlet problem for parabolas ⋮ Polynomial solutions to Dirichlet problems

Cites Work

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• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Homogeneous Partial Derivatives of Radial Functions
• Potential theory

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