Article

Analytic description of the essential spectrum of a family of 3×3 operator matrices

Tulkin H. RasulovFaculty of Physics and Mathematics, Bukhara State University M. Ikbol str. 11, 200100 Bukhara, UzbekistanNargiza Ahmedovna ToshevaFaculty of Physics and Mathematics, Bukhara State University M. Ikbol str. 11, 200100 Bukhara, Uzbekistan

Nanosystems Physics Chemistry Mathematicsjournal2019en

ABI

Abstract

We consider the family of 3 3 operator matrices H(K), K T d := (-; ] d arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus T d . We obtain an analog of the Faddeev equation for the eigenfunctions of H(K). An analytic description of the essential spectrum of H(K) is established. Further, it is shown that the essential spectrum of H(K) consists the union of at most three bounded closed intervals.

Topics

Matrix Theory and Algorithms Holomorphic and Operator Theory Spectral Theory in Mathematical Physics

Identifiers

DOI: 10.17586/2220-8054-2019-10-5-511-519

Citations and references

Cited by 016 references

Metrics — AkademScholar