Please use this identifier to cite or link to this item:
Title: On existence and weak stability of matrix refinable functions
Authors: Jiang, Q. 
Shen, Z. 
Keywords: Refinable function vectors
Stable basis
Issue Date: 1999
Citation: 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
ISSN: 01764276
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

checked on Dec 2, 2021

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.