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   -> Volume 5, Issue 9


Preprint: Multivariate matrix refinable functions
 
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Qingtang Jiang (qjiang@math.nus.sg)
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PostPosted: Thu Oct 10, 1996 1:15 pm    
Subject: Preprint: Multivariate matrix refinable functions
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#2 Preprint: Multivariate matrix refinable functions

Preprint: Multivariate matrix refinable functions with
arbitrary matrix dilation

Author: Qingtang Jiang
Department of Mathematics
National University of Singapore
Lower Kent Ridge Road
Singapore 119260
E-mail : qjiang@haar.math.nus.sg

Abstract: The characterizations of the stability and orthonormality of
the multivariate matrix refinable functions on $R^d$ with matrix
dilations are provided in terms of the eigenvalue and eigenvector
properties of the restricted transition operator. Under mild
conditions, it is obtained that the local approximation order of the
matrix refinable function is equivalent to the order of the vanishing
moment conditions of the matrix refinement mask ${ P_{alpha}}$
. The restricted transition operator is represented by the finite
matrix $(2^{-d}A _{2alpha -eta })_{alpha, eta}$, here
$A_{eta}=sum_{alpha }P _{alpha -eta }otimes P_{alpha }$ and
$P _{alpha -eta }otimes P_{alpha }$ denotes the kronecker product
of matrices $P _{alpha -eta }$, $P_{alpha }$. Some spectral
properties of the transition operator are studied. The Sobolev
regularity estimate of the matrix refinable function is given in terms
of the spectral radius of the restricted transition operator to an
invariant subspace. This estimate is analyzed in an example.

If need a PS. file or a copy of the preprint, send an e-mail to me.
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