TY - JOUR
T1 - Algebraic Properties of Subdivision Operators with Matrix Mask and Their Applications
AU - Chen, Di Rong
PY - 1999/4
Y1 - 1999/4
N2 - 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
AB - 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
KW - Subdivision operator; transition operator; mask; refinable vector; shift-invariant space; approximation order; accuracy; linear independence
UR - https://www.scopus.com/pages/publications/0011935003
U2 - 10.1006/jath.1997.3266
DO - 10.1006/jath.1997.3266
M3 - 文章
AN - SCOPUS:0011935003
SN - 0021-9045
VL - 97
SP - 294
EP - 310
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 2
ER -