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Title: Structural results for quaternionic Gabor frames
Author: Cerejeiras, Paula
Hartmann, Stefan
Orelma, Heikki
Keywords: Quaternionic Gabor frames
Two-sided QWFT
Quaternionic frame operator
Janssen’s representation
Wexler–Raz biorthogonality
Frame bounds
Issue Date: 2018
Publisher: Springer Verlag
Abstract: 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.
Peer review: yes
ISSN: 0188-7009
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Appears in Collections:CHAG - Artigos

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