Finite differrence operators with a finite--band spectrum

2003/09/05 by M. Shapiro, Shapiro, M., V. Vinnikov +3
Mathematics · Physics and Astronomy · #35Q58 #47A48 #47B36 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35Q58 #msc:47A48 #msc:47B36

paper · pdf · doi:10.48550/arxiv.math/0309094

arxiv created 2003/09/20 · arxiv updated 2016/09/07

Abstract

We discuss a functional model for multi--diagonal selfadjoint operators with almost periodic coefficients that generalizes the well known model for finite band Jacobi matrices. It give us an opportunity to construct examples of almost periodic operators with different spectral properties. Main result deals with an exact condition for the uniqueness of the model of the given type.

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