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The Segal–Bargmann Transform on a Symmetric Space of Compact Type

✍ Scribed by Matthew B. Stenzel

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
161 KB
Volume
165
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the Segal Bargmann transform on a symmetric space X of compact type, mapping L 2 (X ) into holomorphic functions on the complexification X C . We invert this transform by integrating against a ``dual'' heat kernel measure in the fibers of a natural fibration of X C over X. We prove that the Segal Bargmann transform is an isometry from L 2 (X ) onto the space of holomorphic functions on X C which are square integrable with respect to a natural measure. These results extend those of B. Hall in the compact group case.

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