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

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.

Document Type

Article

DOI

https://doi.org/10.1023/a:1006712230719

Keywords

Eigenfunction, Jacobi polynomials, Laplacian, Symmetric spaces

Publication Date

1-1-2000

Journal Title

Annals of Global Analysis and Geometry

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