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   -> Volume 6, Issue 8


Preprint: Compactly supported (bi)orthogonal wavelets...
 
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"Zuowei Shen" (matzuows@math.nus.sg)
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PostPosted: Wed Jul 16, 1997 11:21 am    
Subject: Preprint: Compactly supported (bi)orthogonal wavelets...
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#2 Preprint: Compactly supported (bi)orthogonal wavelets...

Title: Compactly supported (bi)orthogonal wavelets generated by
interpolatory refinable functions

Authors: Hui Ji and Zuowei Shen
Department of Mathematics
National University of Singapore
Singapore 119260

Abstract:

This paper provides several constructions of compactly supported
wavelets generated by interpolatory refinable functions. It was shown
in ef{D1} that there is no real compactly supported orthonormal
symmetric dyadic refinable function, except the trivial case; and also
shown in ef{L} and ef{GM} that there is no compactly supported
interpolatory orthonormal dyadic refinable function. Hence, for the
dyadic dilation case, compactly supported wavelets generated by
interpolatory refinable functions have to be biorthogonal wavelets.
The key step to construct the biorthogonal wavelets is to construct a
compactly supported dual function for a given interpolatory refinable
function. We provide two explicit iterative constructions of such
dual functions with desired regularity. When the dilation factors are
larger than $3$, we provide several examples of compactly supported
interpolatory orthonormal symmetric refinable functions from a general
method. This leads to several examples of orthogonal symmetric
(anti-symmetric) wavelets generated by interpolatory refinable
functions.

To get the .ps.Z file:
http://www.math.nus.sg/~matzuows/preprints.html
or by anonymous ftp from approx.math.ualberta.ca in directory
pub/Shen as the file shenji1.ps.Z
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