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.

Full Text

Article Information

Title	On the finiteness of the discrete spectrum of a 3x3 operator matrix
Source	Methods Funct. Anal. Topology, Vol. 22 (2016), no. 1, 48-61
MathSciNet	MR3522861
zbMATH	06630282
Milestones	Received 01/02/2014
Copyright	The 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

Citation Example

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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