Title

Affine Frame Decompositions And Shift-Invariant Spaces

Abstract

In this paper, we show that the property of tight affine frame decomposition of functions in L2 can be extended in a stable way to functions in Sobolev spaces when the generators of the tight affine frames satisfy certain mild regularity and vanishing moment conditions. Applying the affine frame operators Qj on jth levels to any function f in a Sobolev space reveals the detailed information Qjf of f in such tight affine decompositions. We also study certain basic properties of the range of the affine frame operators Qj such as the topological property of closedness and the notion of angles between the ranges for different levels, and thus establishing some interesting connection to (tight) frames of shift-invariant spaces. © 2005 Elsevier Inc. All rights reserved.

Publication Date

1-1-2006

Publication Title

Applied and Computational Harmonic Analysis

Volume

20

Issue

1

Number of Pages

74-107

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.acha.2005.09.003

Socpus ID

32044469424 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/32044469424

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