ANZIAM J. 49 (2007), no. 1, pp. 85–97.

Biorthogonal interpolatory multiscaling functions and corresponding multiwavelets

Shou Zhi Yang
Department of Mathematics
Shantou University
Shantou 515063
P.R. China
szyang@stu.edu.cn.
Received 2 May, 2004; revised 30 June, 2006

Abstract

A method for constructing a pair of biorthogonal interpolatory multiscaling functions is given and an explicit formula for constructing the corresponding biorthogonal multiwavelets is obtained. A multiwavelet sampling theorem is also established. In addition, we improve the stability of the biorthogonal interpolatory multiwavelet frame by the linear combination of a pair of biorthogonal interpolatory multiwavelets. Finally, we give an example illustrating how to use our method to construct biorthogonal interpolatory multiscaling functions and corresponding multiwavelets.

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2000 Mathematics Subject Classification: primary 42C15; secondary 94A12
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2378151 Z'blatt-MATH: pre05243893

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