{"title":"指数基和积分基的解析函数在fr<s:1>切特空间中的逼近","authors":"G. Hassan, A. Atta","doi":"10.21608/aunj.2022.139332.1020","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to establish some theorems on the representation of analytic functions by exponential derived bases and exponential integral bases in Fréchet spaces. Theorems are proven to show such that representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin and for all entire functions. Also, some results concerning the growth order and type of EDBs and EIBs are determined. Moreover, the -property of and are discussed. Finally, some applications to the and of Bernoulli, Euler, Bessel, and Chebyshev polynomials have been studied.","PeriodicalId":8568,"journal":{"name":"Assiut University Journal of Multidisciplinary Scientific Research","volume":"130 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation of analytic functions of exponential derived and integral bases in Fréchet spaces\",\"authors\":\"G. Hassan, A. Atta\",\"doi\":\"10.21608/aunj.2022.139332.1020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to establish some theorems on the representation of analytic functions by exponential derived bases and exponential integral bases in Fréchet spaces. Theorems are proven to show such that representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin and for all entire functions. Also, some results concerning the growth order and type of EDBs and EIBs are determined. Moreover, the -property of and are discussed. Finally, some applications to the and of Bernoulli, Euler, Bessel, and Chebyshev polynomials have been studied.\",\"PeriodicalId\":8568,\"journal\":{\"name\":\"Assiut University Journal of Multidisciplinary Scientific Research\",\"volume\":\"130 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Assiut University Journal of Multidisciplinary Scientific Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21608/aunj.2022.139332.1020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Assiut University Journal of Multidisciplinary Scientific Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21608/aunj.2022.139332.1020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximation of analytic functions of exponential derived and integral bases in Fréchet spaces
The purpose of this paper is to establish some theorems on the representation of analytic functions by exponential derived bases and exponential integral bases in Fréchet spaces. Theorems are proven to show such that representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin and for all entire functions. Also, some results concerning the growth order and type of EDBs and EIBs are determined. Moreover, the -property of and are discussed. Finally, some applications to the and of Bernoulli, Euler, Bessel, and Chebyshev polynomials have been studied.