Segal-Bargmann transform for generalized partial-slice monogenic functions

TL;DR

This paper develops a Segal-Bargmann transform and Schrödinger representation for generalized partial-slice monogenic functions, unifying theories of monogenic and slice monogenic functions over Clifford algebras.

Contribution

It introduces a new transform and representation framework for generalized partial-slice monogenic functions, extending existing theories in Clifford analysis.

Findings

Established the Segal-Bargmann transform in this new setting

Provided a Schrödinger representation for these functions

Utilized the generalized partial-slice Cauchy-Kovalevskaya extension

Abstract

The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to develop the Segal-Bargmann transform and give a Schr\"{o}dinger representation in the setting of generalized partial-slice monogenic functions. To this end, the generalized partial-slice Cauchy-Kovalevskaya extension plays a crucial role.