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Matematicheskie Zametki, 2007, Volume 82, Issue 1, Pages 75–83
DOI: https://doi.org/10.4213/mzm3755 (Mi mzm3755) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Expression for the Number of Eigenvalues of a Friedrichs Model

M. I. Muminov

A. Navoi Samarkand State University
Full-text PDF (450 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm3755
Abstract: We consider the self-adjoint operator of a generalized Friedrichs model whose essential spectrum may contain lacunas. We obtain a formula for the number of eigenvalues lying on an arbitrary interval outside the essential spectrum of this operator. We find a sufficient condition for the discrete spectrum to be finite. Applying the formula for the number of eigenvalues, we show that there exist an infinite number of eigenvalues on the lacuna for a particular Friedrichs model and obtain the asymptotics for the number of eigenvalues.
Keywords: Friedrichs model, self-adjoint operator, essential spectrum of an operator, lacuna, asymptotics for the number of eigenvalues, Weyl's inequality.
Received: 11.01.2006
Revised: 12.02.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 1, Pages 67–74
DOI: https://doi.org/10.1134/S0001434607070097
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: M. I. Muminov, “Expression for the Number of Eigenvalues of a Friedrichs Model”, Mat. Zametki, 82:1 (2007), 75–83; Math. Notes, 82:1 (2007), 67–74
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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