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On the measure of the spectrum of direct integrals

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.

preprint2012arXivOpen access
Anton A. Kutsenko
math.FAmath.SP
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Anton A. Kutsenko

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