Stability of Singular Spectral Types under Decaying Perturbations

2001/10/13 by Alexander Kiselev, A. Kiselev, Yoram Last +6
Computer Science · Mathematics · Physics and Astronomy · #34E10 #34L40 #81Q10 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34E10 #msc:34L40 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math/0110139

25 pages

arxiv created 2001/10/13 · openalex publication_date 2001/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We look at invariance of a.e. boundary condition spectral behavior under perturbations, W, of half-line, continuum or discrete Schrödinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported W's to suitable short-range W. We also discuss invariance of the local Hausdorff dimension of spectral measures under such perturbations.

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