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arXiv · 1911.05555

Analytic description of the essential spectrum of a family of $3 \times 3$ operator matrices

Tulkin H. Rasulov·Nargiza A. Tosheva
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Abstract

We consider the family of $3 \times 3$ operator matrices $H(K),$ $K \in {\Bbb T}^{\rm d}:=(-\pi; \pi]^{\rm d}$ arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus ${\Bbb T}^{\rm d}.$ We obtain an analogue 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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Tulkin H. Rasulov, Nargiza A. Tosheva. 2019-11-13. Analytic description of the essential spectrum of a family of $3 \times 3$ operator matrices. https://arxiv.org/abs/1911.05555

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