The Fourier transform of semi-simple coadjoint orbits
type: Item
instance of: scholarly article
title: The Fourier transform of semi-simple coadjoint orbits
zbMATH Open document ID: 0915.22008
author: Paul-Émile Paradan
published in: Journal of Functional Analysis
publication date: 1999-06-28T00:00:00Z
review text: Let \(M\) be a closed coadjoint orbit of a real connected semisimple Lie group \(G\) and let \(F_M\) be its Fourier transform. The author computes the restriction of \(F_M\) to the Lie algebra \(\mathfrak k\) of a maximal compact subgroup \(K\) of \(G\). Using his technique of localization in equivariant cohomology (to be described in forthcoming papers in \textit{Compositio Mathematica} and \textit{Topology}), he extends previous results of Duflo, Heckman, Vergne, and Sengupta, which dealt with the elliptic and regular cases.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 1278797
zbMATH Keywords: Fourier transform
zbMATH Keywords: coadjoint orbit
zbMATH Keywords: volume form
zbMATH Keywords: localization
reviewed by: William M. McGovern
MaRDI profile type: Publication
full work available at URL: jfan.1998.3381
OpenAlex ID: W2080201319
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DOI: 10.1006/JFAN.1998.3381
description: scientific article; zbMATH DE number 1278797