On the quaternionic short-time Fourier and Segal-Bargmann transforms

Antonino De Martino; Kamal Diki

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arXiv · 2009.00073

On the quaternionic short-time Fourier and Segal-Bargmann transforms

Antonino De Martino·Kamal Diki

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Abstract

In this paper, we study a special one dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal-Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb's uncertainty principle. We provide also the reproducing kernel associated to the Gabor space considered in this setting.

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Antonino De Martino, Kamal Diki. 2020-08-31. On the quaternionic short-time Fourier and Segal-Bargmann transforms. https://arxiv.org/abs/2009.00073

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