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A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type

Published online by Cambridge University Press:  20 November 2018

Brian C. Hall*
Affiliation:
Department of Mathematics, 0112, University of California at San Diego, La Jolla, CA 92093-0112, USA email: bhall@math.ucsd.edu
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Abstract

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I consider a two-parameter family ${{B}_{s,t}}$ of unitary transforms mapping an ${{L}^{2}}$-space over a Lie group of compact type onto a holomorphic ${{L}^{2}}$-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with $\text{B}$. Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting cases $s\,\to \,\infty \,\text{and}\,s\,\to \,t/2$.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1999

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