{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T20:35:42Z","timestamp":1774557342879,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T00:00:00Z","timestamp":1743292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["KFU251253"],"award-info":[{"award-number":["KFU251253"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>One of the best known time\u2013frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we introduce and then study the linear canonical Dunkl windowed transform (LCDWT). Given that localization operators are both theoretically and practically relevant, we will focus in this paper on a number of time\u2013frequency analysis topics for the LCDWT, such as the Lp boundedness and compactness of localization operators for the LCWGT. Then, we study their trace class characterization and show that they are in the Schatten\u2013von Neumann classes. Then, we study their spectral properties in order to give some results on the spectrograms for the LCDWT.<\/jats:p>","DOI":"10.3390\/axioms14040262","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T03:25:02Z","timestamp":1743391502000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Localization Operators for the Linear Canonical Dunkl Windowed Transformation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0606-7305","authenticated-orcid":false,"given":"Saifallah","family":"Ghobber","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia"}]},{"given":"Hatem","family":"Mejjaoli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah Al Munawarah 42353, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0002-9947-1989-0951883-8","article-title":"Differential-difference operators associated to reflection groups","volume":"311","author":"Dunkl","year":"1989","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01244305","article-title":"The Dunkl transform","volume":"113","year":"1993","journal-title":"Invent. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1090\/conm\/138\/1199124","article-title":"Hankel transforms associated to finite reflection groups","volume":"138","author":"Dunkl","year":"1992","journal-title":"Contemp. 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