On the smoothness of mean values of functions with summable spectral expansion
Sh. A. AlimovTashkent Division, Moscow State University, Tashkent, Uzbekistan
ABI
Abstract
We consider spectral expansions associated with a self-adjoint extension of the Laplace operator in the n-dimensional domain. We show that if the spectral expansion of an arbitrary function at some point is summable by Riesz means, then its mean value over the sphere with center at that point has certain smoothness.