Segal–Bargmann transforms and holomorphic Sobolev spaces of fractional order

• Sundaram Thangavelu ^[1]
  1. [1] Indian Institute of Science, India
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 66, Nº. 1, 2023, págs. 297-310
• Idioma: inglés
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• Resumen

  • 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.