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 language||English (US)|
|Number of pages||29|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Jan 1 1994|
ASJC Scopus subject areas
- Applied Mathematics