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Hilbert space valued Gabor frames in wei...
Poria, Anirudha...

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Hilbert space valued Gabor frames in weighted amalgam spaces by Poria, Anirudha ( Author )
Lemonjar Open Access
N.A
07-08-2015
Let H be a separable Hilbert space. In this paper we establish a generalization of Walnut's representation and Janssen's representation of the H−valued Gabor frame operator on H−valued weighted amalgam spaces WH(Lp,Lqv), 1≤p,q≤∞. Also we show that the frame operator is invertible on WH(Lp,Lqv), 1≤p,q≤∞, if the window function is in the Wiener amalgam space WH(L∞,L1w). Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multi-window Gabor frames on WH(Lp,Lqv), 1≤p,q≤∞, as a special case by choosing the appropriate Hilbert space H.
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https://arxiv.org/abs/1508.01646
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