Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/103705
Title: On existence and weak stability of matrix refinable functions
Authors: Jiang, Q. 
Shen, Z. 
Keywords: Refinable function vectors
Stable basis
Issue Date: 1999
Source: Jiang, Q.,Shen, Z. (1999). On existence and weak stability of matrix refinable functions. Constructive Approximation 15 (3) : 337-353. ScholarBank@NUS Repository.
Abstract: We consider the existence of distributional (or L2) solutions of the matrix refinement equation Φ̂ = P(·/2)Φ̂(·/2), where P is an r × r matrix with trigonometric polynomial entries. One of the main results of this paper is that the above matrix refinement equation has a compactly supported distributional solution if and only if the matrix P(0) has an eigenvalue of the form 2n, n ∈ ℤ+. A characterization of the existence of L2-solutions of the above matrix refinement equation in terms of the mask is also given. A concept of L2-weak stability of a (finite) sequence of function vectors is introduced. In the case when the function vectors are solutions of a matrix refinement equation, we characterize this weak stability in terms of the mask.
Source Title: Constructive Approximation
URI: http://scholarbank.nus.edu.sg/handle/10635/103705
ISSN: 01764276
Appears in Collections:Staff Publications

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