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Mat. Sb., 2014, Volume 205, Number 12, Pages 85–98 (Mi msb8305)  

A description of the location and structure of the essential spectrum of a model operator in a subspace of a Fock space

G. R. Yodgorova, F. Ismailb, Z. I. Muminovc

a Navoi State Pedagogical Institute
b Universiti Putra Malaysia
c Malaysia – Japan International Institute of Technology, Kuala Lumpur

Abstract: We consider a certain model operator acting in a subspace of a fermionic Fock space. We obtain an analogue of Faddeev's equation. We describe the location of the essential spectrum of the operator under consideration and show that the essential spectrum consists of the union of at most four segments.
Bibliography: 19 titles.

Keywords: Hamiltonian with a nonconserved bounded number of particles, creation–annihilation operators, essential spectrum, positive operator, Faddeev's equation, compact operator.

Funding Agency Grant Number
Academy of Sciences of the Republic of Uzbekistan ФА-Ф1-Ф045 АН РУз
Universiti Putra Malaysia 5524430

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8305

Full text: PDF file (575 kB)
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English version:
Sbornik: Mathematics, 2014, 205:12, 1761–1774

Bibliographic databases:

UDC: 517.984
MSC: Primary 35P20; Secondary 47N50, 81Q10, 81V70
Received: 19.11.2013 and 25.09.2014

Citation: G. R. Yodgorov, F. Ismail, Z. I. Muminov, “A description of the location and structure of the essential spectrum of a model operator in a subspace of a Fock space”, Mat. Sb., 205:12 (2014), 85–98; Sb. Math., 205:12 (2014), 1761–1774

Citation in format AMSBIB
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