Tight wavelet frames in Lebesgue and Sobolev spaces
We study tight wavelet frame systems in Lp(ℝd) and prove that such systems (under mild hypotheses) give atomic decompositions of Lp(ℝd) for 1≺p≺∞. We also characterize Lp(ℝd) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best m-term approxim...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/792493 |
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| author | L. Borup R. Gribonval M. Nielsen |
| author_facet | L. Borup R. Gribonval M. Nielsen |
| author_sort | L. Borup |
| collection | DOAJ |
| description | We study tight wavelet frame systems in Lp(ℝd) and prove that
such systems (under mild hypotheses) give atomic decompositions of Lp(ℝd) for 1≺p≺∞. We also characterize Lp(ℝd) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best m-term approximation with the systems in Lp(ℝd) and prove that such inequalities exist. Moreover, it is proved that the approximation rate given by the Jackson inequality can be realized by thresholding the frame coefficients. Finally, we
show that in certain restricted cases, the approximation spaces, for best m-term approximation, associated with tight wavelet frames can be characterized in terms of (essentially) Besov spaces. |
| format | Article |
| id | doaj-art-e4a94019ee624693bb4b93ed412cebaa |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-e4a94019ee624693bb4b93ed412cebaa2025-08-20T02:21:34ZengWileyJournal of Function Spaces and Applications0972-68022004-01-012322725210.1155/2004/792493Tight wavelet frames in Lebesgue and Sobolev spacesL. Borup0R. Gribonval1M. Nielsen2Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, DenmarkIRISA-INRIA, Campus de Beaulieu, 35042 Rennes CEDEX, FranceDepartment of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, DenmarkWe study tight wavelet frame systems in Lp(ℝd) and prove that such systems (under mild hypotheses) give atomic decompositions of Lp(ℝd) for 1≺p≺∞. We also characterize Lp(ℝd) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best m-term approximation with the systems in Lp(ℝd) and prove that such inequalities exist. Moreover, it is proved that the approximation rate given by the Jackson inequality can be realized by thresholding the frame coefficients. Finally, we show that in certain restricted cases, the approximation spaces, for best m-term approximation, associated with tight wavelet frames can be characterized in terms of (essentially) Besov spaces.http://dx.doi.org/10.1155/2004/792493 |
| spellingShingle | L. Borup R. Gribonval M. Nielsen Tight wavelet frames in Lebesgue and Sobolev spaces Journal of Function Spaces and Applications |
| title | Tight wavelet frames in Lebesgue and Sobolev spaces |
| title_full | Tight wavelet frames in Lebesgue and Sobolev spaces |
| title_fullStr | Tight wavelet frames in Lebesgue and Sobolev spaces |
| title_full_unstemmed | Tight wavelet frames in Lebesgue and Sobolev spaces |
| title_short | Tight wavelet frames in Lebesgue and Sobolev spaces |
| title_sort | tight wavelet frames in lebesgue and sobolev spaces |
| url | http://dx.doi.org/10.1155/2004/792493 |
| work_keys_str_mv | AT lborup tightwaveletframesinlebesgueandsobolevspaces AT rgribonval tightwaveletframesinlebesgueandsobolevspaces AT mnielsen tightwaveletframesinlebesgueandsobolevspaces |