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.

ON THE POLYANALYTIC SHORT-TIME FOURIER TRANSFORM IN THE QUATERNIONIC SETTING

De Martino, A;
2021-01-01

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.
2021
Short-time Fourier transform
quaternions
slice hyperholomorphic functions
Bargmann transform
slice polyanalytic functions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1256403
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