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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/305961 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549579722063872 |
|---|---|
| author | Xunxiang Guo |
| author_facet | Xunxiang Guo |
| author_sort | Xunxiang Guo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-66c971c4e1a943cc99b6d489bc41dcc8 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-66c971c4e1a943cc99b6d489bc41dcc82025-02-03T06:10:54ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/305961305961Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert SpacesXunxiang Guo0Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaFirstly, 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.http://dx.doi.org/10.1155/2015/305961 |
| spellingShingle | Xunxiang Guo Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces Journal of Function Spaces |
| title | Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces |
| title_full | Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces |
| title_fullStr | Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces |
| title_full_unstemmed | Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces |
| title_short | Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces |
| title_sort | decompositions of g frames and duals and pseudoduals of g frames in hilbert spaces |
| url | http://dx.doi.org/10.1155/2015/305961 |
| work_keys_str_mv | AT xunxiangguo decompositionsofgframesanddualsandpseudodualsofgframesinhilbertspaces |