On the measure of the spectrum of direct integrals

2012/12/02 by Anton A. Kutsenko, Kutsenko, Anton A.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP

paper · pdf · doi:10.48550/arxiv.1212.0235

arxiv created 2012/12/02 · arxiv updated 2012/12/04

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.

Related

• Sharp spectral estimates for periodic matrix-valued Jacobi operators
• Spectral estimates for 2D periodic Jacobi operators
• Note on the spectrum of discrete Schrödinger operators
• Continuity of the measure of the spectrum for discrete quasiperiodic operators
• Schrodinger Operators with Purely Discrete Spectrum