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Title: Stability and orthonormality of multivariate refinable functions
Authors: Lawton, W. 
Lee, S.L. 
Shen, Z. 
Keywords: Dilation matrix
Interpolatory refinable functions
Refinement equations
Subdivision operators
Transition operators
Issue Date: Jul-1997
Citation: Lawton, W.,Lee, S.L.,Shen, Z. (1997-07). Stability and orthonormality of multivariate refinable functions. SIAM Journal on Mathematical Analysis 28 (4) : 999-1014. ScholarBank@NUS Repository.
Abstract: This paper characterizes the stability and orthonormality of the shifts of a multidimensional (M, c) refinable function φ in terms of the eigenvalues and eigenvectors of the transition operator Wcau defined by the autocorrelation cau of its refinement mask c, where M is an arbitrary dilation matrix. Another consequence is that if the shifts of φ form a Riesz basis, then Wcau has a unique eigenvector of eigenvalue 1, and all of its other eigenvalues lie inside the unit circle. The general theory is applied to two-dimensional nonseparable (M, c) refinable functions whose masks are constructed from Daubechies' conjugate quadrature filters.
Source Title: SIAM Journal on Mathematical Analysis
ISSN: 00361410
Appears in Collections:Staff Publications

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