{"title":"A uniqueness theorem for orthonormal spline series","authors":"K. A. Keryan, A. L. Khachatryan","doi":"10.1007/s10474-024-01472-5","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “regular” sequence. Additionally, it is proved that the regularity of the sequence is essential.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"20 - 48"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01472-5","RegionNum":3,"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
We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “regular” sequence. Additionally, it is proved that the regularity of the sequence is essential.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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