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   -> Volume 5, Issue 6

Preprint: Regularity of multiwavelets
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Thomas Sauer (

PostPosted: Tue Aug 06, 1996 9:58 am    
Subject: Preprint: Regularity of multiwavelets
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Preprint: Regularity of multiwavelets

Regularity of multiwvaelets
C.A. Micchelli and T. Sauer

ABSTRACT. The main theme of the paper is to study the regularity of
stable vector fields which satisfy a vector refinement equation with a
finite number of nonzero matrix coefficients. Functions of this type
are known to be the main building block for multiwavelets. By
relating stable refinable vector fields to a suitable subdivision
scheme we obtain charapcterizations of when such a vector field has
derivatives up to a certain order in $L_p$. This characterization is
given in terms of a matrix factorization and a condition on the
spectral radius of the matrix obtained by that factorization. We also
give some comments on vector subdivision schemes in general and show
that for a certain class of vector subdivision schemes a scalar (not
matrix) factorization determines the order of regularity. In a final
section we also show how to construct orthonormal multiwavelets from
orthonormal refinable vector fields by solving the quadrature mirror
filter equation.

A postscript version of the paper (gzip'd) is accessible via my homepage

Thomas Sauer
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