{"title":"矩阵值正交多项式的达尔布等价性","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":"{\"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}","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}
Darboux equivalence for matrix-valued orthogonal polynomials
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
