Work

The Fueter Mittag-Leffler Bargmann transform

Year: 2025

Type: article

Abstract: In this paper we continue exploring the Mittag-Leffler Bargmann (MLB) transform, which maps the Hilbert space L 2 ( R ) onto the Mittag-Leffler-Fock (MLF) space. The MLF space is a reproducing kernel Hilbert space that extends the classic Fock space and its reproducing kernel is given by the Mittag-Leffler function. We study the MLB transform and its main properties in the quaternionic setting. In this noncommutative setting there are two function theories that are prominent: the slice hyperholomorphic theory and the Fueter regular theory. The connection between the slice hyperholomorphic functions and the Fueter regular functions is given by the Fueter mapping theorem. The Mittag-Leffler Bargmann transform investigated in this paper maps the quaternionic-valued L 2 ( R , H ) space onto a counterpart of the MLF space in the Fueter regular setting. Finally the creation, annihilation, backward-shift and integration operators are studied in the case of the Fueter-MLF space.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.129480

Authors: Natanael Alpay, Antonino De Martino, Kamal Diki

Institutions: University of California, Irvine, Ghent University

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Fonds Wetenschappelijk Onderzoek, Vlaamse regering