On the construction of uniformly convergent disk polynomial expansions

DOI10.1007/S13348-010-0017-5zbMath1218.33014OpenAlexW2000001461MaRDI QIDQ545665

Claudemir P. Oliveira, Valdir A. Menegatto, Ana Paula Peron

Publication date: 22 June 2011

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13348-010-0017-5

zbMATH Keywords

Bergman kernelorthogonal expansionsPoisson-Szegő kerneldisk polynomials

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Power series (including lacunary series) in one complex variable (30B10) Spherical harmonics (33C55) Power series, series of functions of several complex variables (32A05) Kernel functions in one complex variable and applications (30C40) Harmonic analysis of several complex variables (32A50)

Related Items (3)

Positive definite functions on complex spheres and their walks through dimensions ⋮ Erratum to: On the construction of uniformly convergent disk polynomial expansions ⋮ On spherical expansions of smooth \(\mathrm{SU}(n)\)-zonal functions on the unit sphere in \(\mathbb C^n\)

Cites Work

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• Banach algebra related to disk polynomials
• Interpolation on the complex Hilbert sphere using positive definite and conditionally negative definite kernels
• Generalized Zernike or disc polynomials
• On spherical expansions of zonal functions on Euclidean spheres
• Spherical Harmonic Expansion of the Poisson-Szego Kernel for the Ball
• Derivation of the shell compatibility equations
• Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)

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