On the generalized Radimacher-Menchoff Theorem - Ahmedov, Anvarjon A.; Matarneh, Ehab (2018)
We consider spectral decompositions of elliptic operators. An analogue of the Radimacher-Menchoff Theorem for general spectral expansions corresponding to a self-adjoint extension of elliptic operators is proved. The theorem obtained allows us to obtain a result on the almost everywhere convergence of the spectral decompositions from the Liouville classes. The sufficient conditions is obtained for spherical summability of multiple Fourier series from Liouville classes Lp (TN); 1 < p < 2, related to the self-adjoint extension of the Laplace operator in torus TN.