On the measure of the spectrum of direct integrals

Published 2 Dec 2012 in math.FA and math.SP | (1212.0235v1)

Abstract: We obtain the estimate of the Lebesgue measure of the spectrum for the direct integral of matrix-valued functions. These estimates are applicable for a wide class of discrete periodic operators. For example: these results give new and sharp spectral bounds for 1D periodic Jacobi matrices and 2D discrete periodic Schrodinger operators.

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Authors (1)

Anton A. Kutsenko

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