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Algebraic Properties of Subdivision Operators with Matrix Mask and Their Applications

✍ Scribed by Di-Rong Chen

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
151 KB
Volume
97
Category
Article
ISSN
0021-9045

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✦ Synopsis

Subdivision operators play an important role in wavelet analysis. This paper studies the algebraic properties of subdivision operators with matrix mask, especially their action on polynomial sequences and on some of their invariant subspaces. As an application, we characterize, under a mild condition, the approximation order provided by refinable vectors in terms of the eigenvalues and eigenvectors of polynomial sequences of the associated subdivision operator. Moreover, some necessary conditions, in terms of nondegeneracy and simplicity of eigenvalues of a matrix related to the subdivision operator for the refinable vector to be smooth are given. The main results are new even in the scalar case.

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