On a characterization of the Rellich–Kondrachov theorem on groups and the Bloch spectral cell equation

Abstract

This paper is concerned with the Rellich–Kondrachov Theorem on Groups. We establish some conditions which characterize in a precise manner important properties related to this theorem and the Sobolev spaces on groups involved on it. The main motivation to study the Rellich–Kondrachov Theorem on Groups comes from the Bloch spectral cell equation, which is an eigenvalue-eigenfunction problem associated with the assymptotic limit of the anisotropic Schrödinger equation.