{"title":"二阶线性微分方程多项式特征函数的 Christoffel-Darboux 公式","authors":"V. E. Kruglov","doi":"10.1134/s0012266124040037","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Using recurrence relations between any three consecutive polynomial eigenfunctions of\nsecond-order linear differential equations, the Christoffel–Darboux formulas are derived for the\nsystem of polynomial eigenfunctions of these equations.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"11 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Christoffel–Darboux Formula for Polynomial Eigenfunctions of Second-Order Linear Differential Equations\",\"authors\":\"V. E. Kruglov\",\"doi\":\"10.1134/s0012266124040037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> Using recurrence relations between any three consecutive polynomial eigenfunctions of\\nsecond-order linear differential equations, the Christoffel–Darboux formulas are derived for the\\nsystem of polynomial eigenfunctions of these equations.\\n</p>\",\"PeriodicalId\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124040037\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124040037","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Christoffel–Darboux Formula for Polynomial Eigenfunctions of Second-Order Linear Differential Equations
Abstract
Using recurrence relations between any three consecutive polynomial eigenfunctions of
second-order linear differential equations, the Christoffel–Darboux formulas are derived for the
system of polynomial eigenfunctions of these equations.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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