Email this article Description of the spectrum of one fourth-order operator matrix
- Authors: Rasulov T.K.1, Latipov H.M.1
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Affiliations:
- Bukhara State University
- Issue: Vol 27, No 3 (2023)
- Pages: 427-445
- Section: Differential Equations and Mathematical Physics
- URL: https://journal-vniispk.ru/1991-8615/article/view/310969
- DOI: https://doi.org/10.14498/vsgtu2003
- ID: 310969
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Abstract
An operator matrix A of fourth-order is considered. This operator corresponds to the Hamiltonian of a system with non conserved number and at most four particles on a lattice. It is shown that the operator matrix A is unitarily equivalent to the diagonal matrix, the diagonal elements of which are operator matrices of fourth-order. The location of the essential spectrum of the operator A is described, that is, two-particle, three-particle and four-particle branches of the essential spectrum of the operator A are singled out. It is established that the essential spectrum of the operator matrix A consists of the union of closed intervals whose number is not over 14. A Fredholm determinant is constructed such that its set of zeros and the discrete spectrum of the operator matrix A coincide, moreover, it was shown that the number of simple eigenvalues of the operator matrix A lying outside the essential spectrum does not exceed 16.
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##article.viewOnOriginalSite##About the authors
Tulkin Kh. Rasulov
Bukhara State University
Author for correspondence.
Email: rth@mail.ru
ORCID iD: 0000-0002-2868-4390
Dr. Sci. (Phys. & Math.), Professor, Vice-Rector for Research and Innovation
Uzbekistan, 705018, Bukhara, Muhammad Ikbol st., 11Hakimboy M. Latipov
Bukhara State University
Email: h.m.latipov@buxdu.uz
ORCID iD: 0000-0002-4806-0155
Assistant Lecturer, Dept. of Mathematical Analysis
Uzbekistan, 705018, Bukhara, Muhammad Ikbol st., 11References
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