{"title":"在x3u = λxv情况下的正则对称除法问题","authors":"M. Mejri, T. Marzouki","doi":"10.1080/10652469.2022.2125964","DOIUrl":null,"url":null,"abstract":"ABSTRACT We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"346 - 363"},"PeriodicalIF":0.7000,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Division problem of a regular symmetric form the case x 3 u = λxv\",\"authors\":\"M. Mejri, T. Marzouki\",\"doi\":\"10.1080/10652469.2022.2125964\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.\",\"PeriodicalId\":54972,\"journal\":{\"name\":\"Integral Transforms and Special Functions\",\"volume\":\"34 1\",\"pages\":\"346 - 363\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Integral Transforms and Special Functions\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/10652469.2022.2125964\",\"RegionNum\":3,\"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":"Integral Transforms and Special Functions","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10652469.2022.2125964","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Division problem of a regular symmetric form the case x 3 u = λxv
ABSTRACT We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.
期刊介绍：
Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.
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