The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators |
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Authors: | Yoram Last Barry Simon |
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Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel;(2) Mathematics 253-37 California Institute of Technology, 91125 Pasadena, CA, USA |
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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.
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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