{"title":"与Toeplitz算子相关的定向短时傅里叶变换及其应用","authors":"Saifallah Ghobber, Hatem Mejjaoli, Slim Omri","doi":"10.1007/s13370-025-01271-3","DOIUrl":null,"url":null,"abstract":"<div><p>In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the <span>\\(L^{p}\\)</span>-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Toeplitz operators associated with the directional short-time Fourier transform and applications\",\"authors\":\"Saifallah Ghobber, Hatem Mejjaoli, Slim Omri\",\"doi\":\"10.1007/s13370-025-01271-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the <span>\\\\(L^{p}\\\\)</span>-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-01-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01271-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01271-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文证明了定向短时傅里叶变换的夏皮罗测不准原理。接下来，我们引入与定向短时傅里叶变换相关的Toeplitz算子的概念。特别地，我们研究了这类算子的迹类性质，并证明了它们属于schaten - von Neumann类。接下来，我们研究了这些Toeplitz算子在\(L^{p}\) -空间中的有界性和紧性。最后，我们介绍并研究了与这些Toeplitz算子相关的广义谱图。
Toeplitz operators associated with the directional short-time Fourier transform and applications
In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the \(L^{p}\)-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
