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|Title:||On existence and weak stability of matrix refinable functions|
|Authors:||Jiang, Q. |
|Keywords:||Refinable function vectors|
|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|
|Appears in Collections:||Staff Publications|
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