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

Autor:	Matthew B. Stenzel
Rok vydání:	1999
Předmět:	Pure mathematics Square-integrable function Compact group Mathematics::Complex Variables Symmetric space Complexification (Lie group) Mathematical analysis Fibration Isometry Holomorphic function Analysis Heat kernel Mathematics
Zdroj:	Journal of Functional Analysis. 165:44-58
ISSN:	0022-1236
DOI:	10.1006/jfan.1999.3396
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e8e20a1bfa8507e4b959e2bb3db94b6 https://doi.org/10.1006/jfan.1999.3396 Zobrazit plný text záznamu Full Text from ScienceDirect