论文标题
Segal-Bargmann转换和霍明型Sobolev空间的分数秩序
Segal-Bargmann transform and holomorphic Sobolev spaces of fractional order
论文作者
论文摘要
在本说明中，我们研究了Segal-Bargmann变换下的紧凑型谎言组$ k $的Sobolev空间的图像。我们表明，可以通过某些加权的伯格曼空间来表征图像在综合中延伸霍尔和lewkeeratiyutkul定理的综合功能上的特征。我们还将处理与Hermite操作员相关的热核转换。
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.
