{"title":"Darboux equivalence for matrix-valued orthogonal polynomials","authors":"Ignacio Bono Parisi, Inés Pacharoni, Ignacio Zurrián","doi":"arxiv-2407.20994","DOIUrl":null,"url":null,"abstract":"In this work, we give some criteria that allow us to decide when two\nsequences of matrix-valued orthogonal polynomials are related via a Darboux\ntransformation and to build explicitly such transformation. In particular, they\nallow us to see when and how any given sequence of polynomials is Darboux\nrelated to a diagonal matrix of classic orthogonal polynomials. We also explore\nthe notion of Darboux-irreducibility and study some sequences that are not a\nDarboux transformation of classical orthogonal polynomials.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.20994","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we give some criteria that allow us to decide when two
sequences of matrix-valued orthogonal polynomials are related via a Darboux
transformation and to build explicitly such transformation. In particular, they
allow us to see when and how any given sequence of polynomials is Darboux
related to a diagonal matrix of classic orthogonal polynomials. We also explore
the notion of Darboux-irreducibility and study some sequences that are not a
Darboux transformation of classical orthogonal polynomials.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
