{"title":"On the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators","authors":"Sunit Ghosh, Jitendriya Swain","doi":"10.1007/s13324-024-00970-7","DOIUrl":null,"url":null,"abstract":"<div><p>The orthonormal Strichartz estimates for the Schrödinger equation associated to the Dunkl Laplacian and the Dunkl-Hermite operator are derived in Senapati et al. (J Geom Anal 34:74, 2024) and Mondal and Song (Israel J Math, 2023). In this article we construct a set of coherent states in the Dunkl setting and apply semi-classical analysis to derive a necessary condition on the Schatten exponent for the aforementioned orthonormal Strichartz estimates, which turns out to be optimal for the Schrödinger equations associated with Laplacian and Hermite operator as a particular case.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00970-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The orthonormal Strichartz estimates for the Schrödinger equation associated to the Dunkl Laplacian and the Dunkl-Hermite operator are derived in Senapati et al. (J Geom Anal 34:74, 2024) and Mondal and Song (Israel J Math, 2023). In this article we construct a set of coherent states in the Dunkl setting and apply semi-classical analysis to derive a necessary condition on the Schatten exponent for the aforementioned orthonormal Strichartz estimates, which turns out to be optimal for the Schrödinger equations associated with Laplacian and Hermite operator as a particular case.
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Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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