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

Vernny Ccajma, Wladimir Neves, Jean Silva
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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.

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关于群上的雷利奇-康德拉乔夫定理的特征和布洛赫谱单元方程
本文关注的是关于群的 Rellich-Kondrachov 定理。我们建立了一些条件,这些条件以精确的方式描述了与该定理相关的重要性质以及与该定理相关的群上的索波列夫空间。研究群上的 Rellich-Kondrachov 定理的主要动机来自布洛赫谱单元方程,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。
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