Geodesic
Analytic description of the essential spectrum of a family of $3\times 3$ operator matrices
Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 5, pp. 511-519

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We consider the family of $3\times 3$ operator matrices $H(K)$, $K\in \mathbb{T}^d:= (-\pi;\pi]^d$ arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus $\mathbb{T}^d$. 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.
Keywords: family of operator matrices, generalized Friedrichs model, bosonic Fock space, annihilation and creation operators, channel operator, decomposable operator, fiber operators, the Faddeev equation, essential spectrum, Weyl criterion. 
@article{NANO_2019_10_5_a1,
     author = {T. H. Rasulov and N. A. Tosheva},
     title = {Analytic description of the essential spectrum of a family of $3\times 3$ operator matrices},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {511--519},
     publisher = {mathdoc},
     volume = {10},
     number = {5},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2019_10_5_a1/}
}
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T. H. Rasulov; N. A. Tosheva. Analytic description of the essential spectrum of a family of $3\times 3$ operator matrices. Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 5, pp. 511-519. http://geodesic.mathdoc.fr/item/NANO_2019_10_5_a1/