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

  Published:1999-08-01
 Printed: Aug 1999
  • Brian C. Hall
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Abstract

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 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 $s \rightarrow \infty$ and $s \rightarrow t/2$.
MSC Classifications: 22E30, 81S30, 58G11 show english descriptions Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Phase-space methods including Wigner distributions, etc.
unknown classification 58G11
22E30 - Analysis on real and complex Lie groups [See also 33C80, 43-XX]
81S30 - Phase-space methods including Wigner distributions, etc.
58G11 - unknown classification 58G11
 

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