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Discrete spectrum of operator valued Friedrichs models. (English) Zbl 0601.45001
The author studies the spectrum of a self-adjoint operator T (operator- valued Friedrichs model) acting on the Hilbert space $$L^ 2(S^ k:H)$$ where $$S^ k$$ is a k-dimensional torus and H is an n-dimensional complex Hilbert space. The operator T is then defined as: $$(Tf)(x)=U(x)f(x)+\int_{S^ k}K(x,y)f(y)dy$$ $$(f\in L^ 2(S^ k:H))$$, where the matrices of order $$n\times n$$ $$U(x)=[U_{ij}(x)]$$ and $$K(x,y)=[K_{ij}(x,y)]$$ are self-adjoint. The author shows that there is only a finite number of eigenvalues of T outside the continuous spectrum of T.
Reviewer: J.Burbea

##### MSC:
 45C05 Eigenvalue problems for integral equations 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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