{"title":"A remark on the Strichartz inequality in one dimension","authors":"R. Frier, Shuanglin Shao","doi":"10.4310/dpde.2022.v19.n2.a4","DOIUrl":null,"url":null,"abstract":"In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on R. We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier space and thus can be extended to be complex analytic. Consequently we provide a new proof to the characterization of the extremal functions: the only extremals are Gaussian functions, which was investigated previously by Foschi [7] and Hundertmark-Zharnitsky [11].","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamics of Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/dpde.2022.v19.n2.a4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on R. We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier space and thus can be extended to be complex analytic. Consequently we provide a new proof to the characterization of the extremal functions: the only extremals are Gaussian functions, which was investigated previously by Foschi [7] and Hundertmark-Zharnitsky [11].
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