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

Annals of Global Analysis and Geometry volume 18, pages 347–369 (2000)Cite this article

Abstract

We find sharp conditions for the pointwise convergence ofeigenfunction expansions associated with the Laplace operator and otherrotationally invariant differential operators. Specifically, we considerthis problem for expansions associated with certain radially symmetricoperators and general boundary conditions and the problem in the contextof Jacobi polynomial expansions. The latter has immediate application toFourier series on rank one symmetric spaces of compact type.

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, IL, 60208–2730, U.S.A.

    Mark A. Pinsky

  2. Department of Mathematics and Statistics, University of Maine, 333 Neville Hall, Orono, ME, 04469–5752, U.S.A.

    William O. Bray

Authors
  1. Mark A. Pinsky
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  2. William O. Bray
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Pinsky, M.A., Bray, W.O. Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type. Annals of Global Analysis and Geometry 18, 347–369 (2000). https://doi.org/10.1023/A:1006712230719

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  • DOI: https://doi.org/10.1023/A:1006712230719

  • eigenfunction
  • Jacobi polynomials
  • Laplacian
  • symmetric spaces