The Poisson kernel for Heisenberg polynomials on the disk

DOI10.1007/BF01174188zbMath0538.43005MaRDI QIDQ793267

Charles F. Dunkl

Publication date: 1984

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173510

zbMATH Keywords

harmonic polynomialsPoisson kernelHeisenberg groupssubelliptic Laplacian

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80) Spherical harmonics (33C55)

Related Items

Fractional Zernike functions ⋮ Hardy spaces for Dunkl-Gegenbauer expansions ⋮ Fredholm property of a family of operators on the five-dimensional Heisenberg group. ⋮ Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry ⋮ Reflection groups and orthogonal polynomials on the sphere ⋮ Uniform treatment of Darboux’s method and the Heisenberg polynomials ⋮ Generalized Zernike polynomials: operational formulae and generating functions

Cites Work

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• The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. I
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
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• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Classical Expansions and Their Relation to Conjugate Harmonic Functions
• The Tangential Cauchy-Riemann Complex on Spheres