Inversion formulas for the Dunkl-type Segal–Bargmann transform

Abstract

We give the inverse of the Dunkl-type Segal–Bargmann transform $B_{\alpha }$ as a limit of certain integral operators. An application to Tikhonov regularization on the Dunkl-type Fock spaces $F_{\alpha }(\mathbb{C})$ is given using the theory of reproducing kernel Hilbert spaces.

Keywords:

• Dunkl-type Fock spaces
• Dunkl-type Segal–Bargmann transform
• extremal functions

2010 Mathematics Subject Classification::

• 32A15
• 32A36
• 46E22

Acknowledgments

Author partially supported by the DGRST research project LR11ES11 and CMCU program 10G/1503

Disclosure statement

No potential conflict of interest was reported by the author.