New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames
We give new characterizations of Riesz-type frames, on equivalent conditions for a continuous frame to be a Riesz-type frame and on equivalency relations between Riesz-type frames and continuous frames. We characterize also the Riesz-type frames by using a bounded linear operator L. Finally, we stud...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/298982 |
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| _version_ | 1832563213814726656 |
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| author | Zhong-Qi Xiang |
| author_facet | Zhong-Qi Xiang |
| author_sort | Zhong-Qi Xiang |
| collection | DOAJ |
| description | We give new characterizations of Riesz-type frames, on equivalent conditions for a continuous frame to be a Riesz-type frame and on equivalency relations between Riesz-type frames and continuous frames. We characterize also the Riesz-type frames by using a bounded linear operator L. Finally, we study the stability of alternate duals of continuous frames and we prove that if two continuous frames are close to each other, then we can find alternate duals of them which are close to each other. |
| format | Article |
| id | doaj-art-4433feaaca2144dfabc6df4c39402c45 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-4433feaaca2144dfabc6df4c39402c452025-02-03T01:20:46ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/298982298982New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous FramesZhong-Qi Xiang0School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, ChinaWe give new characterizations of Riesz-type frames, on equivalent conditions for a continuous frame to be a Riesz-type frame and on equivalency relations between Riesz-type frames and continuous frames. We characterize also the Riesz-type frames by using a bounded linear operator L. Finally, we study the stability of alternate duals of continuous frames and we prove that if two continuous frames are close to each other, then we can find alternate duals of them which are close to each other.http://dx.doi.org/10.1155/2013/298982 |
| spellingShingle | Zhong-Qi Xiang New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames Advances in Mathematical Physics |
| title | New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames |
| title_full | New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames |
| title_fullStr | New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames |
| title_full_unstemmed | New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames |
| title_short | New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames |
| title_sort | new characterizations of riesz type frames and stability of alternate duals of continuous frames |
| url | http://dx.doi.org/10.1155/2013/298982 |
| work_keys_str_mv | AT zhongqixiang newcharacterizationsofriesztypeframesandstabilityofalternatedualsofcontinuousframes |