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.

中文翻译：

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群上 Rellich-Kondachov 定理和 Bloch 谱单元方程的表征

本文涉及群上的 Rellich-Kondachov 定理。我们建立了一些条件，以精确的方式表征与该定理相关的重要属性以及涉及该定理的群的索博列夫空间。研究群上的 Rellich-Kondachov 定理的主要动机来自于 Bloch 谱单元方程，这是一个与各向异性薛定谔方程的渐近极限相关的特征值-特征函数问题。