The Essential Spectrum of Schrödinger, Jacobi, and Cmv Operators
نویسنده
چکیده
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.
منابع مشابه
Essential Closures and Ac Spectra for Reflectionless Cmv, Jacobi, and Schrödinger Operators Revisited
We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application of the notion of the essential closure of subsets of R we revisit the fact that CMV, Jacobi, and Schrödinger operators, reflectionless on a set E of positiv...
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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 polynomial...
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