English

Sobolev spaces on locally compact abelian groups

Mathematical Physics 2012-08-16 v1 High Energy Physics - Theory math.MP

Abstract

Motivated by a class of nonlinear equations of interest for string theory, we introduce Sobolev spaces on arbitrary locally compact abelian groups and we examine some of their properties. Specifically, we focus on analogs of the Sobolev embedding and Rellich- Kondrachov compactness theorems. As an application, we prove the existence of continuous solutions to a generalized euclidean bosonic string equation possed on an arbitrary compact abelian group.

Cite

@article{arxiv.1208.3053,
  title  = {Sobolev spaces on locally compact abelian groups},
  author = {Przemysław Górka and Enrique G. Reyes},
  journal= {arXiv preprint arXiv:1208.3053},
  year   = {2012}
}

Comments

13 pages, submitted on July 2011

R2 v1 2026-06-21T21:50:50.317Z