Journal article ยท Preprint article
On R-Duals and the Duality Principle in Gabor Analysis
The concept of R-duals of a frame was introduced by Casazza, Kutyniok and Lammers in 2004, with the motivation to obtain a general version of the duality principle in Gabor analysis. For tight Gabor frames and Gabor Riesz bases the three authors were actually able to show that the duality principle is a special case of general results for R-duals.
In this paper we introduce various alternative R-duals, with focus on what we call R-duals of type II and III. We show how they are related and provide characterizations of the R-duals of type II and III. In particular, we prove that for tight frames these classes coincide with the R-duals by Casazza et al., which is desirable in the sense that the motivating case of tight Gabor frames already is well covered by these R-duals.
On the other hand, all the introduced types of R-duals generalize the duality principle for larger classes of Gabor frames than just the tight frames and the Riesz bases; in particular, the R-duals of type III cover the duality principle for all Gabor frames.
Language: | English |
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Publisher: | Springer US |
Year: | 2015 |
Pages: | 383-400 |
ISSN: | 15315851 and 10695869 |
Types: | Journal article and Preprint article |
DOI: | 10.1007/s00041-014-9376-8 |
ORCIDs: | Christensen, Ole |