{"title":"双有理傅里叶级数的收敛率","authors":"Hardeepbhai J. Khachar, Rajendra G. Vyas","doi":"10.1007/s11785-023-01479-w","DOIUrl":null,"url":null,"abstract":"<p>We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The rectangular oscillation of the two-variable function is used to quantify this rate. Additionally, we give an approximation of convergence rate of the double rational Fourier series for continuous functions with generalized bounded variation.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"50 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rate of Convergence for Double Rational Fourier Series\",\"authors\":\"Hardeepbhai J. Khachar, Rajendra G. Vyas\",\"doi\":\"10.1007/s11785-023-01479-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The rectangular oscillation of the two-variable function is used to quantify this rate. Additionally, we give an approximation of convergence rate of the double rational Fourier series for continuous functions with generalized bounded variation.</p>\",\"PeriodicalId\":50654,\"journal\":{\"name\":\"Complex Analysis and Operator Theory\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Analysis and Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11785-023-01479-w\",\"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":"Complex Analysis and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-023-01479-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Rate of Convergence for Double Rational Fourier Series
We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The rectangular oscillation of the two-variable function is used to quantify this rate. Additionally, we give an approximation of convergence rate of the double rational Fourier series for continuous functions with generalized bounded variation.
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Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.
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