{"title":"旋转域上的正交多项式","authors":"Yuan Xu","doi":"10.1111/sapm.12703","DOIUrl":null,"url":null,"abstract":"<p>We study orthogonal polynomials (OPs) for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases are provided for weight functions on a number of domains. Particular attention is paid to the setting when an orthogonal basis can be constructed explicitly in terms of known polynomials of either one or two variables. Several new families of OPs are derived, including a few families that are eigenfunctions of a spectral operator and their reproducing kernels satisfy an addition formula.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orthogonal polynomials on domains of revolution\",\"authors\":\"Yuan Xu\",\"doi\":\"10.1111/sapm.12703\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study orthogonal polynomials (OPs) for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases are provided for weight functions on a number of domains. Particular attention is paid to the setting when an orthogonal basis can be constructed explicitly in terms of known polynomials of either one or two variables. Several new families of OPs are derived, including a few families that are eigenfunctions of a spectral operator and their reproducing kernels satisfy an addition formula.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12703\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12703","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
我们研究定义在旋转域上的权函数的正交多项式(OPs),旋转域是由旋转二维区域形成的,并超越了二次域。本文为若干域上的权函数提供了正交基的明确构造。特别关注的是当正交基可以根据已知的一变或二变多项式明确构造时的情况。本文还推导了几个新的 OP 系列,包括几个属于谱算子特征函数的系列,它们的重现核满足加法公式。
We study orthogonal polynomials (OPs) for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases are provided for weight functions on a number of domains. Particular attention is paid to the setting when an orthogonal basis can be constructed explicitly in terms of known polynomials of either one or two variables. Several new families of OPs are derived, including a few families that are eigenfunctions of a spectral operator and their reproducing kernels satisfy an addition formula.