Discrete Schrödinger operators with decaying and oscillating potentials

2021/08/11 by Rupert L. Frank, Frank, Rupert L., Simon Larson +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2108.05083

openalex publication_date 2021/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential V(n)=λn^-αcos(πωn^β), with 1<β<2α, we prove that the spectrum is purely absolutely continuous on the spectrum of the Laplacian.

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