Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the a...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02196913_v12_n2_p_Heineken |
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todo:paper_02196913_v12_n2_p_Heineken2023-10-03T15:11:08Z Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications Heineken, S. Matusiak, E. Paternostro, V. Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces. © 2014 World Scientific Publishing Company. Fil:Heineken, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02196913_v12_n2_p_Heineken |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces |
| spellingShingle |
Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces Heineken, S. Matusiak, E. Paternostro, V. Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications |
| topic_facet |
Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces |
| description |
We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces. © 2014 World Scientific Publishing Company. |
| format |
JOUR |
| author |
Heineken, S. Matusiak, E. Paternostro, V. |
| author_facet |
Heineken, S. Matusiak, E. Paternostro, V. |
| author_sort |
Heineken, S. |
| title |
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications |
| title_short |
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications |
| title_full |
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications |
| title_fullStr |
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications |
| title_full_unstemmed |
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications |
| title_sort |
perturbed frame sequences: canonical dual systems, approximate reconstructions and applications |
| url |
http://hdl.handle.net/20.500.12110/paper_02196913_v12_n2_p_Heineken |
| work_keys_str_mv |
AT heinekens perturbedframesequencescanonicaldualsystemsapproximatereconstructionsandapplications AT matusiake perturbedframesequencescanonicaldualsystemsapproximatereconstructionsandapplications AT paternostrov perturbedframesequencescanonicaldualsystemsapproximatereconstructionsandapplications |
| _version_ |
1782031030477127680 |