Artículo
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
Fecha de publicación:
03/2014
Editorial:
World Scientific
Revista:
International Journal of Wavelets, Multiresolution and Information Processing
ISSN:
0219-6913
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Heineken, Sigrid Bettina; Matusiak, Ewa; Paternostro, Victoria; Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications; World Scientific; International Journal of Wavelets, Multiresolution and Information Processing; 12; 2; 3-2014; 1-17; 1450019
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