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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 3, Pages 518–527
DOI: https://doi.org/10.4213/tmf6107 (Mi tmf6107) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Discrete spectrum of a model operator in Fock space

T. H. Rasulov

A. Navoi Samarkand State University
Full-text PDF (397 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6107
Abstract: We consider a model describing a "truncated" operator (truncated with respect to the number of particles) acting in the direct sum of zero-, one-, and two-particle subspaces of a Fock space. Under some natural conditions on the parameters specifying the model, we prove that the discrete spectrum is finite.
Keywords: discrete spectrum, Fock space, compact operator, continuity in the uniform operator topology, Hilbert–Schmidt operator, Weinberg equation.
Received: 06.11.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 3, Pages 1313–1321
DOI: https://doi.org/10.1007/s11232-007-0115-z
Bibliographic databases:
Language: Russian
Citation: T. H. Rasulov, “Discrete spectrum of a model operator in Fock space”, TMF, 152:3 (2007), 518–527; Theoret. and Math. Phys., 152:3 (2007), 1313–1321
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf6107
  • https://doi.org/10.4213/tmf6107
  • https://www.mathnet.ru/eng/tmf/v152/i3/p518
    • This publication is cited in the following 4 articles:
    1. M. Muminov, H. Neidhardt, T. Rasulov, “On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case”, Journal of Mathematical Physics, 56:5 (2015)  crossref
    2. T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, Theoret. and Math. Phys., 164:1 (2010), 883–895  mathnet  crossref  crossref  adsnasa  isi
    3. Rasulov T.H., “Investigations of the Essential Spectrum of a Hamiltonian in Fock Space”, Applied Mathematics & Information Sciences, 4:3 (2010), 395–412  mathscinet  isi
    4. T. H. Rasulov, “Investigation of the spectrum of a model operator in a Fock space”, Theoret. and Math. Phys., 161:2 (2009), 1460–1470  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:425
    Full-text PDF :211
    References:54
    First page:2
     
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