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- Title
ON THE POLYANALYTIC SHORT-TIME FOURIER TRANSFORM IN THE QUATERNIONIC SETTING.
- Authors
DE MARTINO, ANTONINO; DIKI, KAMAL
- Abstract
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions. Indeed, we will use the notions of true and full slice polyanalytic Fock spaces and Segal-Bargmann transforms. We prove new properties of this QSTFT including a Moyal formula, a reconstruction formula and a Lieb's uncertainty principle. These results extend a recent paper of the authors which studies a QSTFT having a Gaussian function as a window.
- Subjects
FOURIER transforms; FOCK spaces; HEISENBERG uncertainty principle; QUATERNION functions; GAUSSIAN function
- Publication
Communications on Pure & Applied Analysis, 2022, Vol 21, Issue 11, p3629
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2022117