{"title":"用细化掩模进行逼近","authors":"E. A. Lebedeva","doi":"10.1134/s0001434624030076","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We construct a Parseval wavelet frame with compact support for an arbitrary continuous <span>\\(2\\pi\\)</span>-periodic function <span>\\(f\\)</span>, <span>\\(f(0)=1\\)</span>, satisfying the inequality <span>\\(|f(x)|^2+|f(x+\\pi)|^2\\le 1\\)</span>. The frame refinement mask uniformly approximates <span>\\(f\\)</span>. The refining function has stable integer shifts. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation by Refinement Masks\",\"authors\":\"E. A. Lebedeva\",\"doi\":\"10.1134/s0001434624030076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We construct a Parseval wavelet frame with compact support for an arbitrary continuous <span>\\\\(2\\\\pi\\\\)</span>-periodic function <span>\\\\(f\\\\)</span>, <span>\\\\(f(0)=1\\\\)</span>, satisfying the inequality <span>\\\\(|f(x)|^2+|f(x+\\\\pi)|^2\\\\le 1\\\\)</span>. The frame refinement mask uniformly approximates <span>\\\\(f\\\\)</span>. The refining function has stable integer shifts. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0001434624030076\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624030076","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We construct a Parseval wavelet frame with compact support for an arbitrary continuous \(2\pi\)-periodic function \(f\), \(f(0)=1\), satisfying the inequality \(|f(x)|^2+|f(x+\pi)|^2\le 1\). The frame refinement mask uniformly approximates \(f\). The refining function has stable integer shifts.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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