Pointwise fourier inversion and related eigenfunction expansions

Mark A. Pinsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Necessary and sufficient conditions are found for the convergence at a pre‐assigned point of the spherical partial sums (resp. integrals) of the Fourier series (resp. integral) in the class of piecewise smooth functions on Euclidean space. These results carry over unchanged to spherical harmonic expansions, Fourier transforms on hyperbolic space, and Dirichlet eigenfunction expansions with respect to the Laplace operator on a class of Riemannian manifolds. © 1994 John Wiley & Sons, Inc.

Original languageEnglish (US)
Pages (from-to)653-681
Number of pages29
JournalCommunications on Pure and Applied Mathematics
Volume47
Issue number5
DOIs
StatePublished - Jan 1 1994

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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