On the essential spectrum of elliptic differential operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Georgescu, Vladimir¹ 

[1] Univ Cergy Pontoise, Dept Math, F-95000 Cergy Pontoise, France

关键词: Spectral analysis;    Essential spectrum;    Fredholm;    C*-algebra;    Crossed product;   

DOI  :  10.1016/j.jmaa.2018.08.042

来源: Elsevier

【 摘 要 】

Let A be a C*-algebra of bounded uniformly continuous functions on a finite dimensional real vector space X such that A is stable under translations and contains the continuous functions that have a limit at infinity. Denote A(dagger) the boundary of X in the character space of A. Then to each operator A in the crossed product A (sic) X one may naturally associate a family of bounded operators A(aleph) on L-2(X) indexed by the characters aleph is an element of A(dagger). We show that the essential spectrum of A is the union of the spectra of the operators A(aleph). The applications cover very general classes of singular elliptic operators. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free