Orthogonal Polynomials with a Singularly Perturbed Airy Weight

IF 1 3区 数学 Q1 MATHEMATICS Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-08-12 DOI:10.1007/s40840-024-01753-w
Chao Min, Yuan Cheng
{"title":"Orthogonal Polynomials with a Singularly Perturbed Airy Weight","authors":"Chao Min, Yuan Cheng","doi":"10.1007/s40840-024-01753-w","DOIUrl":null,"url":null,"abstract":"<p>We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail’s ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity.\n</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"18 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Malaysian Mathematical Sciences Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01753-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail’s ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity.

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
具有奇异扰动空气权重的正交多项式
我们研究了关于奇异扰动艾里权重的单次正交多项式。通过使用 Chen 和 Ismail 的梯形算子方法,我们推导出了一个由正交多项式的递推系数所满足的离散系统。我们发现正交多项式满足一个二阶线性常微分方程,其系数都用递推系数表示。通过考虑时间演化,我们得到了一个由递推系数满足的微分差分方程组。最后,我们研究了当正交多项式的度数趋于无穷大时递推系数的渐近线。
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 去求助
来源期刊
CiteScore
2.40
自引率
8.30%
发文量
176
审稿时长
3 months
期刊介绍: This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.
期刊最新文献
Two Supercongruences Involving Truncated Hypergeometric Series Data-Driven Wavelet Estimations for Density Derivatives Traveling Wave Solutions in Temporally Discrete Lotka-Volterra Competitive Systems with Delays On the $$\textrm{v}$$ -number of Gorenstein Ideals and Frobenius Powers Existence of Nodal Solutions with Arbitrary Number of Nodes for Kirchhoff Type Equations
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1