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

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.

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