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Eigenfunction expansions and the pinsky phenomenon on compact manifolds

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Abstract

We extend results on pointwise convergence of eigenfunction expansions established for functions on flat tori in [24] and [26] to the setting of compact Riemannian manifolds, subject to a mild restriction on the order of caustics that can arise in the fundamental solution of the wave equation. This gives analyses of some endpoint cases of results treated in [3]. In particular, we are able to treat the Pinsky phenomenon for eigenfunction expansions of piecewise smooth functions with jump across the boundary of a ball on such manifolds, in dimension three.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, 27599, Chapel Hill, NC

    Michael Taylor

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  1. Michael Taylor
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Communicated by Fulvio Ricci

Acknowledgements and Notes. Partially supported by NSF grant DMS 9877077.

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Taylor, M. Eigenfunction expansions and the pinsky phenomenon on compact manifolds. The Journal of Fourier Analysis and Applications 7, 507–522 (2001). https://doi.org/10.1007/BF02511223

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  • DOI: https://doi.org/10.1007/BF02511223

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