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The finite section method and problems in frame theory

Authors
Publisher
Academic Press
Publication Date
Keywords
  • Localized Frame
  • Finite Section Method
  • Frames
  • Shift-Invariant System
  • Inverse Frame Operator
Disciplines
  • Computer Science

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.

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