Polar decomposition and isometric integral transforms^∗

^∗Supported by NSF of China, Grant Number 1990/036.

Abstract

Bargmann transform is the isometry part in the polar decomposition of the restriction operation from

holomorphic functions on complex space to functions on real space .The coherent state transforms recently discovered by Hall (J.Funt . Anal .122, 1994) and the Weyl correspondence are also of this nature

Keywords:

• polar decomposition
• Bargmann transform
• heat semi-group
• coherent states Weyl correspondence

MSC(1991):

• 43A32
• 47B38
• 814R30

^∗Supported by NSF of China, Grant Number 1990/036.

^∗Supported by NSF of China, Grant Number 1990/036.

Notes

^∗Supported by NSF of China, Grant Number 1990/036.

Additional information

Notes on contributors

Shunlong Luo