Journal article
On the Duality Principle by Casazza, Kutyniok, and Lammers
The R-dual sequences of a frame {f i } i∈I , introduced by Casazza, Kutyniok and Lammers in (J. Fourier Anal. Appl. 10(4):383–408, 2004), provide a powerful tool in the analysis of duality relations in general frame theory. In this paper we derive conditions for a sequence {ω j } j∈I to be an R-dual of a given frame {f i } i∈I .
In particular we show that the R-duals {ω j } j∈I can be characterized in terms of frame properties of an associated sequence {n i } i∈I . We also derive the duality results obtained for tight Gabor frames in (Casazza et al. in J. Fourier Anal. Appl. 10(4):383–408, 2004) as a special case of a general statement for R-duals of frames in Hilbert spaces.
Finally we consider a relaxation of the R-dual setup of independent interest. Several examples illustrate the results.
Language: | English |
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Publisher: | SP Birkhäuser Verlag Boston |
Year: | 2011 |
Pages: | 640-655 |
ISSN: | 15315851 and 10695869 |
Types: | Journal article |
DOI: | 10.1007/s00041-010-9151-4 |
ORCIDs: | Christensen, Ole |