{"title":"The Whittaker Plancherel theorem","authors":"","doi":"10.1007/s11537-023-2230-5","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>The purpose of this article is to give an exposition of a proof of the distributional form of the Whittaker Plancherel Theorem. The proof is an application of Harish-Chandra’s Plancherel Theorem for real reductive groups and its exposition can be used as an introduction to Harish-Chandra’s Plancherel Theorem. The paper follows the basic method in the author’s original approach in his second volume on real reductive groups. An error in the calculation of the Whittaker Transform of a Harish-Chandra wave packet is fixed using a result of Raphaël Beuzart-Plessis.</p>","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11537-023-2230-5","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 purpose of this article is to give an exposition of a proof of the distributional form of the Whittaker Plancherel Theorem. The proof is an application of Harish-Chandra’s Plancherel Theorem for real reductive groups and its exposition can be used as an introduction to Harish-Chandra’s Plancherel Theorem. The paper follows the basic method in the author’s original approach in his second volume on real reductive groups. An error in the calculation of the Whittaker Transform of a Harish-Chandra wave packet is fixed using a result of Raphaël Beuzart-Plessis.
期刊介绍：
The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years.
An eminent international mathematics journal, the Japanese Journal of Mathematics has been published since 1924. It is an ideal resource for a wide range of mathematicians extending beyond a small circle of specialists.
The official journal of the Mathematical Society of Japan.
Devoted to authoritative research survey articles that will promote future progress in mathematics.
Gives new insight on topics of current interest from broad perspectives and/or reviews all major developments in an important area over many years.
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