Structural results for quaternionic Gabor frames

We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well...

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Bibliographic Details
Main Author: Cerejeiras, Paula (author)
Other Authors: Hartmann, Stefan (author), Orelma, Heikki (author)
Format: article
Language:eng
Published: 2019
Subjects:
Quaternionic Gabor frames
Two-sided QWFT
Quaternionic frame operator
Janssen’s representation
Wexler–Raz biorthogonality
Frame bounds
Online Access:http://hdl.handle.net/10773/24151
Country:Portugal
Oai:oai:ria.ua.pt:10773/24151
Description
Summary:We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well as modified versions of the Wexler–Raz biorthogonality and Ron–Shen duality based on the concept of correlation function. We end up with a characterization of tight quaternionic Gabor frames.

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