World Scientific
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

PERTURBED FRAME SEQUENCES: CANONICAL DUAL SYSTEMS, APPROXIMATE RECONSTRUCTIONS AND APPLICATIONS

    https://doi.org/10.1142/S0219691314500192Cited by:3 (Source: Crossref)

    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.

    AMSC: 42C40, 42C15