Generalized Appell polynomials and Fueter-Bargmann transforms in the polyanalytic setting
Antonino De Martino, Kamal Diki
TL;DR
This paper introduces generalized Appell polynomials derived from polyanalytic Fueter mappings in quaternionic analysis, characterizes their range on Fock spaces, and explores associated Fueter-Bargmann transforms.
Contribution
It develops a new family of polynomials and characterizes the Fueter-Bargmann transforms in the polyanalytic quaternionic setting, extending existing analysis tools.
Findings
Construction of generalized Appell polynomials
Characterization of Fueter mapping ranges on Fock spaces
Analysis of polyanalytic Fueter-Bargmann transforms
Abstract
Tnis paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings it is possible to construct a new family of polynomials which are called the generalized Appell polynomials. Furthermore, the range of the polyanalytic Fueter mappings on two different polyanalytic Fock spaces is characterized. Finally, we study the polyanalytic Fueter-Bargmann transforms.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods