论文信息 - The Segal–Bargmann Transform on a Symmetric Space of Compact Type☆

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

Abstract 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.

Matthew B. Stenzel

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