On the Pinsky Phenomenon for B-Elliptic Operators

Abstract

Necessary conditions for the summability of spectral expansions in eigenfunctions of an elliptic operator with a Bessel operator in one of the variables in an arbitrary-dimensional domain adjacent to the singularity hypersurface are obtained. It is proved that if the spectral expansion of an arbitrary function at some point of this hypersurface is summable by Riesz means, then its average value over the half-ball centered at the specified point has generalized smoothness.