{"title":"On an Approximation by Band-Limited Functions","authors":"Yu. A. Kriksin, V. F. Tishkin","doi":"10.1134/S1064562424602312","DOIUrl":null,"url":null,"abstract":"<p>The problem of approximating a continuous real function of one real variable defined on an interval using a band-limited function based on Tikhonov’s regularization method is considered. Numerical estimates of the accuracy of such approximations are calculated for a model trigonometric function. We analyze why a theoretical estimate for the approximation accuracy of a continuous function by band-limited functions is difficult to achieve numerically. The problem of estimating the spectrum of a signal defined on a finite interval is discussed.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 3","pages":"500 - 505"},"PeriodicalIF":0.5000,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424602312","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The problem of approximating a continuous real function of one real variable defined on an interval using a band-limited function based on Tikhonov’s regularization method is considered. Numerical estimates of the accuracy of such approximations are calculated for a model trigonometric function. We analyze why a theoretical estimate for the approximation accuracy of a continuous function by band-limited functions is difficult to achieve numerically. The problem of estimating the spectrum of a signal defined on a finite interval is discussed.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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