IMAS 23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
artículos
Título:
Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
Autor/es:
HEINEKEN SIGRID; MATUSIAK EWA; PATERNOSTRO VICTORIA
Revista:
International Journal of Wavelets, Multiresolution and Information Processing
Editorial:
WORLD SCIENTIFIC PUBL CO PTE LTD
Referencias:
Lugar: London, UK; Año: 2014
ISSN:
0219-6913
Resumen:
We consider perturbation of frames and frame sequences in a Hilbert space H. 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(Rd). 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.
