Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces
Firstly, we study the representation of g-frames in terms of linear combinations of simpler ones such as g-orthonormal bases, g-Riesz bases, and normalized tight g-frames. Then, we study the dual and pseudodual of g-frames, which are critical components in reconstructions. In particular, we characte...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/305961 |
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| Summary: | Firstly, we study the representation of g-frames in terms of linear combinations of simpler ones such as g-orthonormal bases, g-Riesz bases, and normalized tight g-frames. Then, we study the dual and pseudodual of g-frames, which are critical components in reconstructions. In particular, we characterize the dual g-frames in a constructive way; that is, the formulae for dual g-frames are given. We also give some g-frame like representations for pseudodual g-frame pairs. The operator parameterizations of g-frames and decompositions of bounded operators are the key tools to prove our main results. |
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| ISSN: | 2314-8896 2314-8888 |