The Cholewinski-Fock space in the Slice Hyperholomorphic Setting

Abstract

Inspired from the Cholewinski approach see [5], we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well as some associated quaternionic linear operators. In a particular case, we reobtain the slice hyperholomorphic Fock space introduced and studied in [2].

arXiv commentTo appear in Mathematical Methods in the Applied Sciences

References in corpus (6)

• Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators
• Segal-Bargmann-Fock modules of monogenic functions
• A Representation of Weyl-Heisenberg Lie Algebra in the Quaternionic Setting
• Extending coherent state transforms to Clifford analysis
• Coherent State Transforms and the Weyl Equation in Clifford Analysis
• On the Bargmann-Radon transform in the monogenic setting

Cited by in corpus (2)

• Generalized Fock spaces and the Stirling numbers
• Segal-Bargmann transform for generalized partial-slice monogenic functions