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arXiv · 2008.03910

Segal-Bargmann transform and holomorphic Sobolev spaces of fractional order

Sundaram Thangavelu
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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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Sundaram Thangavelu. 2020-08-10. Segal-Bargmann transform and holomorphic Sobolev spaces of fractional order. https://arxiv.org/abs/2008.03910

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