On the generalized Radimacher-Menchoff Theorem for general spectral decomposition of the elliptic differential operators

Abstract

The spectral decompositions of elliptic operators are considered. An analogue of the Radimacher-Menchoff Theorem for general spectral expansions corresponding to a self-adjoint extension of elliptic operators is obtained. The theorem obtained allows us to obtain a result on the almost everywhere convergence of the spectral decompositions from the Liouville classes. The estimation of the maximal operator corresponding to the spherical sums of multiple Fourier series from Liouville classes , 1 ⩽ p ⩽ 2, is derived.