On summability of eigenfunction expansions of piecewise smooth functions

Abstract

We consider two forms of eigenfunction expansions associated with an arbitrary elliptic differential operator with constant coefficients and order m, that is the multiple Fourier series and integrals. For the multiple Fourier integrals, we prove the convergence of the Riesz means of order s > (N − 3)/2 of piecewise smooth functions of N ≥ 2 variables. The same result is proved in the case of the N ≥ 3 dimensional multiple Fourier series.