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.
Citation
Anton A. Kutsenko. "On the measure of the spectrum of direct integrals." Banach J. Math. Anal. 9 (2) 1 - 8, 2015. https://doi.org/10.15352/bjma/09-2-1
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