Discrete Schrödinger operators with decaying and oscillating potentials

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1803

R. Frank, S. Larson

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引用次数: 0

Abstract

The paper is devoted to a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential V ( n ) = λ n − α cos ⁡ ( π ω n β ) V(n)=\lambda n^{-\alpha }\cos (\pi \omega n^\beta ) with 1 > β > 2 α 1>\beta >2\alpha , it is proved that the spectrum is purely absolutely continuous on the spectrum of the Laplacian.

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具有衰变和振荡势的离散薛定谔算子

本文主要讨论了具有快速振荡的幂级数衰变势的离散一维薛定谔算子族。特别是，对于 1 > β > 2 α 1>\beta >2\alpha 的势 V ( n ) = λ n - α cos ( π ω n β ) V(n)=\lambda n^{-\alpha }cos (\pi \omega n^\beta ) ，证明了其频谱在拉普拉卡频谱上是纯粹绝对连续的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.