On the discrete spectrum of the nonanalygic matrix-valued Friedrichs model (Q1264745)
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scientific article
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| English | On the discrete spectrum of the nonanalygic matrix-valued Friedrichs model |
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On the discrete spectrum of the nonanalygic matrix-valued Friedrichs model (English)
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12 September 1999
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The authors deal with a selfadjoint operator \(H\) acting in the Hilbert space \(L^2\), according to the formula: \[ \left( Hf \right) (x) = U(x)f(x) + \int_{\mathbb T^\nu} K(x,y)f(y) \text{ d} y \] where \({\mathbb T^\nu}\) is a \(\nu\)-dimensional torus. They establish the finiteness of the discrete spectrum of \(H\) for a broader class of complex matrices \(U(x)\) and \(K(x,y)\).
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discrete spectrum
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essential spectrum
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nonanalytic matrix coefficients
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selfadjoint operator
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