najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2019-10-5-511-519najo-583Research ArticleMATHEMATICSМАТЕМАТИКАAnalytic description of the essential spectrum of a family of 3x3 operator matricesRasulovT. H.

M. Ikbol str. 11, 200100 Bukhara

 

rth@mail.ruToshevaN. A.

M. Ikbol str. 11, 200100 Bukhara

nargiza_n@mail.ruBukhara State University, Faculty of Physics and MathematicsUzbekistan201923082025105511519Copyright © Rasulov T.H., Tosheva N.A., 20252025Rasulov T.H., Tosheva N.A.Rasulov T.H., Tosheva N.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/583

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.

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The authors declare that there are no conflicts of interest present.