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   -> Volume 7, Issue 10


Preprint: Compactly Supported Refinable Functions with Infinite Masks
 
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Vasily Strela (strela@emmy.dartmouth.edu)
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PostPosted: Thu Dec 05, 2002 9:24 am    
Subject: Preprint: Compactly Supported Refinable Functions with Infinite Masks
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#7 Preprint: Compactly Supported Refinable Functions with Infinite Masks

Title: Compactly Supported Refinable Functions with Infinite Masks

Authors: Gilbert Strang, Vasily Strela, and Ding-Xuan Zhou

Abstract: A compactly supported scaling function can come from a
refinement equation with infinitely many nonzero coefficients (an
infinite mask). In this case we prove that the symbol of the mask
must have the special rational form $ ilde a(Z)= ilde b(Z^2) ilde
c(Z)/ ilde b(Z)$. Any finite combination of the shifts of a
refinable function will have such a mask, and will be refinable.

We also study compactly supported solutions of vector refinement
equations with infinite masks. Our characterization is based on the
two-scale similarity transform which plays an essential role in the
investigation of multiple wavelets. This concept is used to
characterize refinable subspaces of refinable shift-invariant spaces.
One advantage of our approach is to provide the refinement masks
for generators of refinable subspaces.

Tha paper can be found at
http://pascal.dartmouth.edu/~strela
or
http://www-math.mit.edu/~gs
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