{"title":"Growth properties of Hartley transform via moduli of continuity","authors":"Nurbek Kakharman, Niyaz Tokmagambetov","doi":"10.1007/s11868-024-00628-9","DOIUrl":null,"url":null,"abstract":"<p>This study investigates the relationship between the moduli of continuity of a function and its Hartley transform. We explore this connection by deriving significant results such as the Riemann–Lebesgue lemma, Parseval’s theorem, and the Hausdorff–Young inequality for the Hartley transform in both the Euclidean space and torus. Using a translation operator, we obtain an analog of Titchmarsh’s theorem for the Hartley transform. In addition, we extend our analysis to the Hartley series on the torus.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"36 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pseudo-Differential Operators and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11868-024-00628-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This study investigates the relationship between the moduli of continuity of a function and its Hartley transform. We explore this connection by deriving significant results such as the Riemann–Lebesgue lemma, Parseval’s theorem, and the Hausdorff–Young inequality for the Hartley transform in both the Euclidean space and torus. Using a translation operator, we obtain an analog of Titchmarsh’s theorem for the Hartley transform. In addition, we extend our analysis to the Hartley series on the torus.
期刊介绍:
The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.