The essential spectrum of Schrödinger, Jacobi, and CMV operators

Yoram Last; Barry Simon

doi:10.1007/BF02790275

The essential spectrum of Schrödinger, Jacobi, and CMV operators

Yoram Last^*, Barry Simon

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

65 Scopus citations

Abstract

We provide a very general result which identifies the essential spectrum of broad classes of operators as exactly equal to the closure of the union of the spectra of suitable limits at infinity. Included is a new result on the essential spectra when potentials are asymptotic to isospectral tori. We also recover within a unified framework the HVZ Theorem and Krein's results on orthogonal polynomials with finite essential spectra.

Original language	English
Pages (from-to)	183-220
Number of pages	38
Journal	Journal d'Analyse Mathematique
Volume	98
DOIs	https://doi.org/10.1007/BF02790275
State	Published - 2006

Bibliographical note

Funding Information:
*Supported in part by The Israel Science Foundation (grant No. 188/02). t Supported in part by NSF grant DMS-0140592. ~Research supported in part by grant No. 2002068 from the United States-Israel Binafional Science Foundation (BSF), Jerusalem, Israel

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The essential spectrum of Schrödinger, Jacobi, and CMV operators

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