Journal d’Analyse Mathématique

, Volume 98, Issue 1, pp 183–220

The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators



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.


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© The Hebrew University Magnes Press 2006

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Mathematics 253-37 California Institute of TechnologyPasadenaUSA

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