Conference paper
Operator representations of frames
The purpose of this paper is to consider representations of frames {fk}k∈I in a Hilbert space ℋ of the form {fk}k∈I = {Tkf0}k∈I for a linear operator T; here the index set I is either ℤ or ℒ0. While a representation of this form is available under weak conditions on the frame, the analysis of the properties of the operator T requires more work.
For example it is a delicate issue to obtain a representation with a bounded operator, and the availability of such a representation not only depends on the frame considered as a set, but also on the chosen indexing. Using results from operator theory we show that by embedding the Hilbert space ℋ into a larger Hilbert space, we can always represent a frame via iterations of a bounded operator, composed with the orthogonal projection onto ℋ.
The paper closes with a discussion of an open problem concerning representations of Gabor frames via iterations of a bounded operator.
Language: | English |
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Publisher: | IEEE |
Year: | 2017 |
Pages: | 207-11 |
Proceedings: | 2017 International Conference on Sampling Theory and Applications |
ISBN: | 1538615649 , 1538615657 , 1538615665 , 9781538615645 , 9781538615652 and 9781538615669 |
Types: | Conference paper |
DOI: | 10.1109/SAMPTA.2017.8024348 |
ORCIDs: | Christensen, Ole and Hasannasab, Marzieh |