The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2006Embargo end date: 01 Mar 2005 United States English Publisher:Springer Science and Business Media LLCJournal:Journal d'Analyse Mathématique, volume 98, pages 183-220 (issn: 0021-7670, eissn: 1565-8538,

Copyright policy )Funded by:NSF | Problems in Mathematical ...

Authors: Last, Yoram; Simon, Barry;

doi: 10.1007/bf02790275 , 10.48550/arxiv.math/0503391

arXiv: math/0503391

The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators

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Abstract

We provide a very general result that 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 with a unified framework the HVZ theorem and Krein's results on orthogonal polynomials with finite essential spectra.

Country

United States

Related Organizations

California Institute of Technology
United States
Hebrew University of Jerusalem
Israel

Keywords

Schrödinger operator, essential spectrum, FOS: Physical sciences, General topics in linear spectral theory for PDEs, Mathematical Physics (math-ph), General spectral theory of ordinary differential operators, HUZ theorem, 510, Mathematics - Spectral Theory, FOS: Mathematics, Spectrum, resolvent, Spectral Theory (math.SP), Mathematical Physics, 47A10, 35J10, 47B36

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