The finite section method and problems in frame theory

Authors:
Ole Christensen;Thomas Strohmer
Affiliations:
Technical University of Denmark, Department of Mathematics, Building 303, 2800 Lyngby, Denmark;University of California, Department of Mathematics, 1 Shields Ave. Davis, CA
Venue:
Journal of Approximation Theory
Year:
2005

Citing 3
Cited 1

Ten lectures on wavelets

Ten lectures on wavelets
Approximation of the inverse frame operator and applications to Gabor frames

Journal of Approximation Theory
Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces

SIAM Review

Optimal adaptive computations in the Jaffard algebra and localized frames

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz basis.