Segal–Bargmann transforms and holomorphic Sobolev spaces of fractional order

Authors

  • Sundaram Thangavelu Department of Mathematics, Indian Institute of Science, 560 012 Bangalore, India

DOI:

https://doi.org/10.33044/revuma.4363

Abstract

In this note we investigate the image of Sobolev spaces of fractional order on a compact Lie group $K$ under the Segal–Bargmann transform. We show that the image can be characterised in terms of certain weighted Bergman spaces of holomorphic functions on the complexification extending a theorem of Hall and Lewkeeratiyutkul. We also treat the heat kernel transform associated to the Hermite operator.

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Published

2023-09-21