Some Results for the Two-Sided Quaternionic Gabor Fourier Transform and Quaternionic Gabor Frame Operator

In this paper, we first present some properties of the two-sided quaternionic Gabor Fourier transform (QGFT) on quaternion valued function space L 2 ( R 2 , H ) , such as Parseval’s formula and the characterization of the range of the two-sided QGFT. Then, we give the definitions of quaternionic Wie...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2021-02, Vol.31 (1), Article 1
Main Authors: Li, Jinxia, He, Jianxun
Format: Article
Language:English
Subjects:
Applications of Mathematics
Fourier transforms
Function space
Mathematical and Computational Physics
Mathematical Methods in Physics
Metric space
Operators (mathematics)
Physics
Physics and Astronomy
Quaternions
Theoretical
Walnuts
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Summary:In this paper, we first present some properties of the two-sided quaternionic Gabor Fourier transform (QGFT) on quaternion valued function space L 2 ( R 2 , H ) , such as Parseval’s formula and the characterization of the range of the two-sided QGFT. Then, we give the definitions of quaternionic Wiener space and quaternionic Gabor frame operator (QGFO), which are the generalizations in the quaternionic settings. Finally, we prove Walnut’s and Janssen’s representation theorems and other boundedness results of the QGFO.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-020-01101-8