Banach Journal of Mathematical Analysis

On the measure of the spectrum of direct integrals

Anton A. Kutsenko

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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.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 2 (2015), 1-8.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419001100

Digital Object Identifier
doi:10.15352/bjma/09-2-1

Mathematical Reviews number (MathSciNet)
MR3296101

Zentralblatt MATH identifier
1310.47005

Subjects
Primary: 47A10: Spectrum, resolvent
Secondary: 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds

Keywords
Direct integral Jacobi matrix spectral estimates measure of spectrum

Citation

Kutsenko, Anton A. On the measure of the spectrum of direct integrals. Banach J. Math. Anal. 9 (2015), no. 2, 1--8. doi:10.15352/bjma/09-2-1. https://projecteuclid.org/euclid.bjma/1419001100


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