{"title":"矩阵值柯西双正交多项式与一种新的非交换可积格","authors":"Shi-Hao Li, Ying Shi, Guo-Fu Yu, Jun-Xiao Zhao","doi":"10.1111/sapm.70040","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Matrix-valued Cauchy bi-orthogonal polynomials are proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in the four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials satisfy a novel noncommutative integrable system, whose Lax pair is given by fractional differential operators with non-abelian variables.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Matrix-Valued Cauchy Bi-Orthogonal Polynomials and a Novel Noncommutative Integrable Lattice\",\"authors\":\"Shi-Hao Li, Ying Shi, Guo-Fu Yu, Jun-Xiao Zhao\",\"doi\":\"10.1111/sapm.70040\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>Matrix-valued Cauchy bi-orthogonal polynomials are proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in the four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials satisfy a novel noncommutative integrable system, whose Lax pair is given by fractional differential operators with non-abelian variables.</p></div>\",\"PeriodicalId\":51174,\"journal\":{\"name\":\"Studies in Applied Mathematics\",\"volume\":\"154 3\",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2025-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studies in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/sapm.70040\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.70040","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Matrix-Valued Cauchy Bi-Orthogonal Polynomials and a Novel Noncommutative Integrable Lattice
Matrix-valued Cauchy bi-orthogonal polynomials are proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in the four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials satisfy a novel noncommutative integrable system, whose Lax pair is given by fractional differential operators with non-abelian variables.
期刊介绍：
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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