Localization of spherical harmonic expansions

DOI10.1007/BF01536909zbMath0543.43006MaRDI QIDQ796029

Christopher Meaney

Publication date: 1984

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178191

zbMATH Keywords

Laplace-Beltrami operatorlocalizationJacobi polynomialpseudofunctionsspherical harmonic expansiontwo-point homogeneous spaceRiemann-Lebesgue setzonal function

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Spherical harmonics (33C55) Uniqueness and localization for orthogonal series (42C25)

Related Items (6)

Localization for Riesz means of Fourier expansions ⋮ Strict positive definiteness on products of compact two-point homogeneous spaces ⋮ Divergent Jacobi Polynomial Series ⋮ The principle of general localization on unit sphere ⋮ Summation by Riesz means of the Fourier-Laplace series ⋮ Slepian spatial-spectral concentration on the ball

Cites Work

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• Absence of localization of the Laplace series on the sphere for functions of the Nikol'skii class \(H^1_1(S^2)\)
• Regularity and integrability of spherical means
• Almost-everywhere convergence of expansions in eigenfunctions of the Laplace operator in the sphere
• The addition formula for the eigenfunctions of the Laplacian
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Fourier series of differentiable functions on SU(2)
• Two-point homogeneous spaces
• Localization on Spheres
• Divergent Jacobi Polynomial Series
• Gaussian processes on compact symmetric spaces
• Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques

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