The Rellich Lemma on Compact Abelian Groups and Equations of Infinite Order

Partially motivated by a class of nonlinear equations of interest for string theory, cosmology and p-adic analysis, we continue our research on Sobolev spaces on arbitrary locally compact abelian (LCA) groups. In this paper we focus on an analog for LCA groups of the classical Rellich compactness theorem. As an application, we prove the existence of continuous solutions to a generalized Euclidean bosonic string equation posed on a compact abelian group. © 2013 World Scientific Publishing Company.