On the Quaternionic Short-Time Fourier and Segal–Bargmann Transforms-Reference-Cited by-同舟云学术

On the Quaternionic Short-Time Fourier and Segal–Bargmann Transforms

Published:2021-04-19 Issue:3 Volume:18 Page:
ISSN:1660-5446
Container-title:Mediterranean Journal of Mathematics
language:en
Short-container-title:Mediterr. J. Math.

Author:

De Martino Antonino^ORCID,Diki Kamal^ORCID

Abstract

AbstractIn 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 with the Gabor space considered in this setting.

Funder

INdAM

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00009-021-01745-1.pdf

Reference27 articles.

1. Abreu, L.D., Feichtinger, H.G.: Function Spaces of Polyanalytic Functions, Harmonic and Complex Analysis and Its Applications, 1–38. Trends Math. Birkhäuser/Springer, Cham (2014)

2. Alpay, D., Colombo, F., Sabadini, I., Salomon, G.: The Fock space in the slice hyperholomorphic Setting. In: Hypercomplex Analysis: New perspectives and applications. Trends Math. pp. 43–59 (2014)

3. Alpay, D., Colombo, F., Sabadini, I.: Slice Hyperholomorphic Schur Analysis Operator. Theory: Advances and Applications, vol. 256. Birkhäuser, Basel (2017)

4. Alpay, D., Diki, K., Sabadini, I.: On slice polyanalytic functions of a quaternionic variable. Res. Math. 74, 17 (2019)

5. Bahri, M., Ashino, R.: Two-Dimensional Quaternionic Window Fourier Transform, in Fourier Transform—Approach to Scientific Principles. InTechOpen, London (2011)

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