The inverse Segal-Bargmann transform for compact Lie groups
type: Item
instance of: scholarly article
title: The inverse Segal-Bargmann transform for compact Lie groups
zbMATH Open document ID: 0869.22005
author: Brian C. Hall
published in: Journal of Functional Analysis
publication date: 1997-08-31T00:00:00Z
review text: In a preceding paper [ibid. 122, 103-151 (1994; Zbl 0838.22004)] the author introduced a generalized Segal-Bargmann transform on an arbitrary compact connected Lie group \(K\), together with an inversion formula. Here he describes a new inversion formula which is obtained by taking a holomorphic function \(F(g)\) on the complexification \(K_\mathbb{C}\) of \(K\), fixing the real part of \(g\), and integrating over the imaginary axis with respect to a certain heat kernel measure. In a sense, a formula for the inverse heat operator on a compact Lie group is obtained in this way. This formula allows to give a new proof of the unitary character of the \(K\)-invariant form of the Segal-Bargmann transform.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 997635
zbMATH Keywords: Segal-Bargmann transform
zbMATH Keywords: Lie group
zbMATH Keywords: inversion formula
zbMATH Keywords: holomorphic function
zbMATH Keywords: complexification
zbMATH Keywords: heat kernel measure
reviewed by: G. Loupias
MaRDI profile type: Publication
full work available at URL: jfan.1996.2954
OpenAlex ID: W2013582185
DOI: 10.1006/JFAN.1996.2954
description: scientific article; zbMATH DE number 997635