Open Access
2015 On the measure of the spectrum of direct integrals
Anton A. Kutsenko
Banach J. Math. Anal. 9(2): 1-8 (2015). DOI: 10.15352/bjma/09-2-1


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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Anton A. Kutsenko. "On the measure of the spectrum of direct integrals." Banach J. Math. Anal. 9 (2) 1 - 8, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1310.47005
MathSciNet: MR3296101
Digital Object Identifier: 10.15352/bjma/09-2-1

Primary: 47A10
Secondary: 34L15 , 47B36

Keywords: Direct integral , Jacobi matrix , measure of spectrum , spectral estimates

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
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