Gabor duality theory for Morita equivalent C*-algebras
Journal article, Peer reviewed
Published version
Permanent lenke
https://hdl.handle.net/11250/2680072Utgivelsesdato
2020Metadata
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- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38672]
Originalversjon
https://doi.org/10.1142/S0129167X20500731Sammendrag
The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalence bimodules with some extra properties. For certain twisted group C∗-algebras, the reformulation of the duality principle to the setting of Morita equivalence bimodules reduces to the well-known Gabor duality principle by localizing with respect to a trace. We may lift all results at the module level to matrix algebras and matrix modules, and in doing so, it is natural to introduce (n,d)-matrix Gabor frames, which generalize multi-window super Gabor frames. We are also able to establish density theorems for module frames on equivalence bimodules, and these localize to density theorems for (n,d)-matrix Gabor frames.