2007/11/26 by Jan Janas, Serguei Naboko, Janas, Jan +3
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #47B36 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Lanthanide and Transition Metal Complexes #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:47B36 #msc:81Q10
paper · pdf · doi:10.48550/arxiv.0711.4035
This is a substantially revised and expanded version of 0711.4035v1
openalex publication_date 2007/11/26 · arxiv created 2008/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bounds on the exponential decay of generalized eigenfunctions of bounded and unbounded selfadjoint Jacobi matrices are established. Two cases are considered separately: (i) the case in which the spectral parameter lies in a general gap of the spectrum of the Jacobi matrix and (ii) the case of a lower semi-bounded Jacobi matrix with values of the spectral parameter below the spectrum. It is demonstrated by examples that both results are sharp. We apply these results to obtain a "many barriers-type" criterion for the existence of square-summable generalized eigenfunctions of an unbounded Jacobi matrix at almost every value of the spectral parameter in suitable open sets. As an application, we provide examples of unbounded Jacobi matrices with a spectral mobility edge.