Weyl asymptotics for perturbations of Morse potential and connections to the Riemann zeta function

IF 0.3 Q4 MATHEMATICS
R. Rahm
{"title":"Weyl asymptotics for perturbations of Morse potential and connections to the Riemann zeta function","authors":"R. Rahm","doi":"10.1515/conop-2022-0139","DOIUrl":null,"url":null,"abstract":"Abstract Let N ( T ; V ) N\\left(T;\\hspace{0.33em}V) denote the number of eigenvalues of the Schrödinger operator − y ″ + V y -{y}^{^{\\prime\\prime} }+Vy with absolute value less than T T . This article studies the Weyl asymptotics of perturbations of the Schrödinger operator − y ″ + 1 4 e 2 t y -{y}^{^{\\prime\\prime} }+\\frac{1}{4}{e}^{2t}y on [ x 0 , ∞ ) \\left[{x}_{0},\\infty ) . In particular, we show that perturbations by functions ε ( t ) \\varepsilon \\left(t) that satisfy ∣ ε ( t ) ∣ ≲ e t | \\varepsilon \\left(t)| \\hspace{0.33em}\\lesssim \\hspace{0.33em}{e}^{t} do not change the Weyl asymptotics very much. Special emphasis is placed on connections to the asymptotics of the zeros of the Riemann zeta function.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"10 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2022-0139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract Let N ( T ; V ) N\left(T;\hspace{0.33em}V) denote the number of eigenvalues of the Schrödinger operator − y ″ + V y -{y}^{^{\prime\prime} }+Vy with absolute value less than T T . This article studies the Weyl asymptotics of perturbations of the Schrödinger operator − y ″ + 1 4 e 2 t y -{y}^{^{\prime\prime} }+\frac{1}{4}{e}^{2t}y on [ x 0 , ∞ ) \left[{x}_{0},\infty ) . In particular, we show that perturbations by functions ε ( t ) \varepsilon \left(t) that satisfy ∣ ε ( t ) ∣ ≲ e t | \varepsilon \left(t)| \hspace{0.33em}\lesssim \hspace{0.33em}{e}^{t} do not change the Weyl asymptotics very much. Special emphasis is placed on connections to the asymptotics of the zeros of the Riemann zeta function.
Morse势扰动的Weyl渐近性及其与Riemann-zeta函数的联系
抽象设N(T;V)N\left(T;\space{0.33em}V)表示Schrödinger算子−y〃+Vy-{y}^{^{\prime\prime}}+Vy的绝对值小于T的特征值的个数。本文研究Schrödinger算子−y〃+14e2t y-{y}^的扰动的Weyl渐近性^{2t}y在[x 0,∞)\left[{x}_{0},\infty)。特别地,我们证明了函数ε(t)\varepsilon\left(t)的扰动,其满足Şε(t。特别强调了与黎曼ζ函数的零的渐近性的联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信