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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

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