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The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators

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.

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Correspondence to Yoram Last.

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Supported in part by The Israel Science Foundation (grant No. 188/02).

Supported in part by NSF grant DMS-01 40592.

Research supported in part by grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

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Last, Y., Simon, B. The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators. J. Anal. Math. 98, 183–220 (2006). https://doi.org/10.1007/BF02790275

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Keywords

  • Orthogonal Polynomial
  • Limit Point
  • Trial Function
  • Essential Spectrum
  • Selfadjoint Operator