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On the finiteness of the discrete spectrum of a 3x3 operator matrix


Abstract

An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra of two families of the generalized Friedrichs models. A symmetric version of the Weinberg equation for eigenvectors of $H$ is obtained. The conditions which guarantee the finiteness of the number of discrete eigenvalues located below the bottom of the three-particle branch of the essential spectrum of $H$ is found.

Key words: Operator matrix, bosonic Fock space, annihilation and creation operators, generalized Friedrichs model, essential and discrete spectra, Weinberg equation, continuity in the uniform operator topology.


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Article Information

TitleOn the finiteness of the discrete spectrum of a 3x3 operator matrix
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 1, 48-61
MathSciNet MR3522861
zbMATH 06630282
MilestonesReceived 01/02/2014
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

Tulkin H. Rasulov
Faculty of Physics and Mathematics, Bukhara State University, 11 M. Ikbol str., Bukhara, 200100, Uzbekistan


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Tulkin H. Rasulov, On the finiteness of the discrete spectrum of a 3x3 operator matrix, Methods Funct. Anal. Topology 22 (2016), no. 1, 48-61.


BibTex

@article {MFAT844,
    AUTHOR = {Rasulov, Tulkin H.},
     TITLE = {On the finiteness of the discrete spectrum of a
3x3 operator matrix},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {48-61},
      ISSN = {1029-3531},
  MRNUMBER = {MR3522861},
 ZBLNUMBER = {06630282},
       URL = {http://mfat.imath.kiev.ua/article/?id=844},
}


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