Segal–Bargmann transforms and holomorphic Sobolev spaces of fractional order
DOI:
https://doi.org/10.33044/revuma.4363Abstract
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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