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Pointwise fourier inversion and related eigenfunction expansions
Author(s) -
Pinsky Mark A.
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470504
Subject(s) - mathematics , eigenfunction , mathematical analysis , fourier series , spherical harmonics , fourier transform , pointwise , dirichlet distribution , pointwise convergence , pure mathematics , eigenvalues and eigenvectors , boundary value problem , approx , physics , quantum mechanics , computer science , operating system
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.