Segal-Bargmann-Fock modules of monogenic functions

Abstract

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.

11 pages

References in corpus (2)

• Extending coherent state transforms to Clifford analysis
• Coherent State Transforms and the Weyl Equation in Clifford Analysis

Cited by in corpus (8)

• On the Bargmann-Fock-Fueter and Bergman-Fueter integral transforms
• On the Bargmann-Radon transform in the monogenic setting
• The Cholewinski-Fock space in the Slice Hyperholomorphic Setting
• On the Mittag Leffler Bargmann (MLB) transform
• New aspects of Bargmann transform using Touchard polynomials and hypergeometric functions
• Clifford Coherent State Transforms on Spheres
• On the Bergman kernel in weighted monogenic Bargmann-Fock spaces
• Segal-Bargmann transform for generalized partial-slice monogenic functions