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arXiv · 1509.06263

On various R-duals and the duality principle

Diana T. Stoeva·Ole Christensen
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Abstract

The duality principle states that a Gabor system is a frame if and only if the corresponding adjoint Gabor system is a Riesz sequence. In general Hilbert spaces and without the assumption of any particular structure, Casazza, Kutyniok and Lammers have introduced the so-called R-duals that also lead to a characterization of frames in terms of associated Riesz sequences; however, it is still an open question whether this abstract theory is a generalization of the duality principle. In this paper we prove that a modified version of the R-duals leads to a generalization of the duality principle that keeps all the attractive properties of the R-duals. In order to provide extra insight into the relations between a given sequence and its R-duals, we characterize all the types of R-duals that are available in the literature for the special case where the underlying sequence is a Riesz basis.

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Diana T. Stoeva, Ole Christensen. 2015-09-21. On various R-duals and the duality principle. https://doi.org/10.1007/s00020-016-2283-4

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