Analytic description of the essential spectrum of a family of 3x3 operator matrices
https://doi.org/10.17586/2220-8054-2019-10-5-511-519
Abstract
We consider the family of 3 х 3 operator matrices H(K), K ϵ Td := (-π; π]d arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus Td. 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.
About the Authors
T. H. Rasulov
Bukhara State University, Faculty of Physics and Mathematics
Uzbekistan
Uzbekistan
T.H. Rasulov
M. Ikbol str. 11, 200100 Bukhara
N. A. Tosheva
Bukhara State University, Faculty of Physics and Mathematics
Uzbekistan
Uzbekistan
N. A. Tosheva
M. Ikbol str. 11, 200100 Bukhara
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Review
For citations:
Rasulov T.H., Tosheva N.A. Analytic description of the essential spectrum of a family of 3x3 operator matrices. Nanosystems: Physics, Chemistry, Mathematics. 2019;10(5):511-519. https://doi.org/10.17586/2220-8054-2019-10-5-511-519
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