Title

Super-Wavelets And Decomposable Wavelet Frames

Keywords

Decomposable and extendable Parseval wavelet frames; Super-wavelet; Wavelet

Abstract

A wavelet frame is called decomposable whenever it is equivalent to a superwavelet frame of length greater than one. Decomposable wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there exists a Parseval wavelet frame which is m-decomposable for any 1 < m ≤ n, but not k-decomposable for any k > n. Moreover, there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m ≤ n, but can not be extended to any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given. © 2005 Birkhäuser Boston. All rights reserved.

Publication Date

12-1-2005

Publication Title

Journal of Fourier Analysis and Applications

Volume

11

Issue

6

Number of Pages

683-696

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00041-005-5005-x

Socpus ID

29644445940 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/29644445940

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