On Gabor g-frames an Fourier series of operators
Peer reviewed, Journal article
Accepted version
Permanent lenke
https://hdl.handle.net/11250/2989153Utgivelsesdato
2021Metadata
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- Institutt for matematiske fag [2533]
- Publikasjoner fra CRIStin - NTNU [38576]
Sammendrag
We show that Hilbert–Schmidt operators can be used to define frame-like structures for L2(Rd) over lattices in R2d that include multi-window Gabor frames as a special case. These frame-like structures are called Gabor g-frames, since they are examples of g-frames as introduced by Sun. We show that Gabor g-frames share many properties of Gabor frames, including a Janssen representation and Wexler–Raz biorthogonality conditions. A central part of our analysis is a notion of Fourier series of periodic operators based on earlier work by Feichtinger and Kozek, where we show in particular a Poisson summation formula for trace class operators. By choosing operators from certain Banach subspaces of the Hilbert–Schmidt operators, Gabor g-frames give equivalent norms for modulation spaces in terms of weighted ℓp-norms of an associated sequence, as previously shown for localization operators by Dörfler, Feichtinger and Gröchenig.