HILBERT SPACES OF HOLOMORPHIC FUNCTIONS ON COMPLEX LIE GROUPS (Joint with L. Gross)(To appear in the Proceedings of the 1994 Taniguchi Symposium.)An isometry is established between a Hilbert space of holomorphic, square integrable functions with respect to the heat kernel measure on a simply connected, complex Lie group and a Hilbert space of ``expansion coefficients'' of such functions at the identity of the group. The manuscript is available as a LaTeX file (77K) and as a DVI file (112K). To LaTex this file you will need the following style file: sprocl.sty. (5K) August 9, 1996

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