Sampling Formulas Involving Differences in Shift-Invariant Subspaces: A Unified Approach. (26th April 2018)

• Record Type: Journal Article
• Authors: García, Antonio G.; Muñoz-Bouzo, María J.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 6(2018)
• Page Start: 667
• Page End: 688
• Publication Date: 2018-04-26
• Subjects: Averages -- dual Riesz bases -- forward and backward differences -- sampling formulas -- shift-invariant subspaces; 42C15 -- 94A20 -- 97N50; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1406946
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Successive differences on a sequence of data help discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper is to mimic them to a sequence of regular samples of a function in a shift-invariant subspace allowing its stable recovery. A suitable expression for the functions in the shift-invariant subspace by an isomorphism with the L 2 (0, 1) space is the key to identify the simple pattern followed by the dual Riesz bases involved in the derived formulas. The paper contains examples illustrating different non-exhaustive situations including also the two-dimensional case.