Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type

Mark A. Pinsky; William O. Bray

doi:10.1023/a:1006712230719

Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type

Mark A. Pinsky^*, William O. Bray

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We find sharp conditions for the pointwise convergence of eigenfunction expansions associated with the Laplace operator and other rotationally invariant differential operators. Specifically, we consider this problem for expansions associated with certain radially symmetric operators and general boundary conditions and the problem in the context of Jacobi polynomial expansions. The latter has immediate application to Fourier series on rank one symmetric spaces of compact type.

Original language	English (US)
Pages (from-to)	347-369
Number of pages	23
Journal	Annals of Global Analysis and Geometry
Volume	18
Issue number	3-4
DOIs	https://doi.org/10.1023/a:1006712230719
State	Published - Jan 1 2000

Keywords

Eigenfunction
Jacobi polynomials
Laplacian
Symmetric spaces

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

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10.1023/a:1006712230719

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abstract = "We find sharp conditions for the pointwise convergence of eigenfunction expansions associated with the Laplace operator and other rotationally invariant differential operators. Specifically, we consider this problem for expansions associated with certain radially symmetric operators and general boundary conditions and the problem in the context of Jacobi polynomial expansions. The latter has immediate application to Fourier series on rank one symmetric spaces of compact type.",

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AU - Pinsky, Mark A.

AU - Bray, William O.

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N2 - We find sharp conditions for the pointwise convergence of eigenfunction expansions associated with the Laplace operator and other rotationally invariant differential operators. Specifically, we consider this problem for expansions associated with certain radially symmetric operators and general boundary conditions and the problem in the context of Jacobi polynomial expansions. The latter has immediate application to Fourier series on rank one symmetric spaces of compact type.

AB - We find sharp conditions for the pointwise convergence of eigenfunction expansions associated with the Laplace operator and other rotationally invariant differential operators. Specifically, we consider this problem for expansions associated with certain radially symmetric operators and general boundary conditions and the problem in the context of Jacobi polynomial expansions. The latter has immediate application to Fourier series on rank one symmetric spaces of compact type.

KW - Eigenfunction

KW - Jacobi polynomials

KW - Laplacian

KW - Symmetric spaces

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ER -

Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type

Abstract

Keywords

ASJC Scopus subject areas

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