Essential spectrum of perturbed pseudodifferential operators. applications to the schrödinger, Klein-Gordon, and dirac operators

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Abstract

The aim of the paper is to present a new approach to the investigation of the essential spectrum of Schrödinger, Klein-Gordon, and Dirac operators. We include these operators in the class of pseudodifferential operators perturbed by nonsmooth potentials. For an operator under consideration, we introduce a family of limit operators and prove that the essential spectrum of the original operator is the union of the spectra of limit operators. Because the limit operators have a simpler structure than the original operator, we obtain a powerful tool for investigating the essential spectra of differential and pseudodifferential operators. We apply this method to the study of the essential spectrum of the Schrödinger, Klein-Gordon, and Dirac operators. Copyright © 2005 by MAIK "Nauka/Interperiodica" (Russia).
Original languageAmerican English
Pages (from-to)62-80
Number of pages53
JournalRussian Journal of Mathematical Physics
StatePublished - 1 Jan 2005

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Essential Spectrum
Dirac Operator
Pseudodifferential Operators
operators
Operator
Differential operator
Union
unions
differential operators

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title = "Essential spectrum of perturbed pseudodifferential operators. applications to the schr{\"o}dinger, Klein-Gordon, and dirac operators",
abstract = "The aim of the paper is to present a new approach to the investigation of the essential spectrum of Schr{\"o}dinger, Klein-Gordon, and Dirac operators. We include these operators in the class of pseudodifferential operators perturbed by nonsmooth potentials. For an operator under consideration, we introduce a family of limit operators and prove that the essential spectrum of the original operator is the union of the spectra of limit operators. Because the limit operators have a simpler structure than the original operator, we obtain a powerful tool for investigating the essential spectra of differential and pseudodifferential operators. We apply this method to the study of the essential spectrum of the Schr{\"o}dinger, Klein-Gordon, and Dirac operators. Copyright {\circledC} 2005 by MAIK {"}Nauka/Interperiodica{"} (Russia).",
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N2 - The aim of the paper is to present a new approach to the investigation of the essential spectrum of Schrödinger, Klein-Gordon, and Dirac operators. We include these operators in the class of pseudodifferential operators perturbed by nonsmooth potentials. For an operator under consideration, we introduce a family of limit operators and prove that the essential spectrum of the original operator is the union of the spectra of limit operators. Because the limit operators have a simpler structure than the original operator, we obtain a powerful tool for investigating the essential spectra of differential and pseudodifferential operators. We apply this method to the study of the essential spectrum of the Schrödinger, Klein-Gordon, and Dirac operators. Copyright © 2005 by MAIK "Nauka/Interperiodica" (Russia).

AB - The aim of the paper is to present a new approach to the investigation of the essential spectrum of Schrödinger, Klein-Gordon, and Dirac operators. We include these operators in the class of pseudodifferential operators perturbed by nonsmooth potentials. For an operator under consideration, we introduce a family of limit operators and prove that the essential spectrum of the original operator is the union of the spectra of limit operators. Because the limit operators have a simpler structure than the original operator, we obtain a powerful tool for investigating the essential spectra of differential and pseudodifferential operators. We apply this method to the study of the essential spectrum of the Schrödinger, Klein-Gordon, and Dirac operators. Copyright © 2005 by MAIK "Nauka/Interperiodica" (Russia).

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