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On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

Published online by Cambridge University Press:  20 November 2018

Ole Christensen ,
Hong Oh Kim  and
Rae Young Kim
Ole Christensen
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Lyngby, Denmark e-mail: ochr@dtu.dk
Hong Oh Kim
Affiliation:
Department of Mathematical Sciences, KAIST Guseong-dong, Yuseong-gu, Daejeon, 305-701, Republic of Korea e-mail: kimhong@kaist.edu
Rae Young Kim
Affiliation:
Department of Mathematics, Yeungnam University, Dae-dong, Gyeongsan-si, Gyeongsangbuk-do, 712-749, Republic of Korea e-mail: rykim@ynu.ac.kr
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Abstract

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The unitary extension principle $\left( \text{UEP} \right)$ by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the $\text{UEP}$ -type wavelet systems that can be extended to a Parseval wavelet frame by adding just one $\text{UEP}$ -type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

Keywords

42C1542C40Bessel sequencesframesextension of wavelet Bessel system to tight framewavelet systemsunitary extension principle

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 254 - 263
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

This research was supported by the Yeungnam University research grants in 2010.

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