{"title":"矩阵Nevanlinna- pick插值的Nevanlinna公式","authors":"Yury Dyukarev","doi":"10.1016/j.laa.2025.01.007","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study the matrix Nevanlinna-Pick interpolation problem in the completely indeterminate case. We obtain an explicit formula for the resolvent matrix in terms of rational matrix functions of the first and second kind. Additionally, we describe the set of all solutions to the matrix Nevanlinna-Pick interpolation problem using linear fractional transformations applied to Nevanlinna pairs. This result can be viewed as an analogue of the Nevanlinna formula for the matrix Hamburger moment problem.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"709 ","pages":"Pages 241-270"},"PeriodicalIF":1.1000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Nevanlinna formula for matrix Nevanlinna-Pick interpolation\",\"authors\":\"Yury Dyukarev\",\"doi\":\"10.1016/j.laa.2025.01.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we study the matrix Nevanlinna-Pick interpolation problem in the completely indeterminate case. We obtain an explicit formula for the resolvent matrix in terms of rational matrix functions of the first and second kind. Additionally, we describe the set of all solutions to the matrix Nevanlinna-Pick interpolation problem using linear fractional transformations applied to Nevanlinna pairs. This result can be viewed as an analogue of the Nevanlinna formula for the matrix Hamburger moment problem.</div></div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":\"709 \",\"pages\":\"Pages 241-270\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2025-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379525000072\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/17 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379525000072","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/17 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Nevanlinna formula for matrix Nevanlinna-Pick interpolation
In this paper, we study the matrix Nevanlinna-Pick interpolation problem in the completely indeterminate case. We obtain an explicit formula for the resolvent matrix in terms of rational matrix functions of the first and second kind. Additionally, we describe the set of all solutions to the matrix Nevanlinna-Pick interpolation problem using linear fractional transformations applied to Nevanlinna pairs. This result can be viewed as an analogue of the Nevanlinna formula for the matrix Hamburger moment problem.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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