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Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 747-762, 2007
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Matrix refinement equations:

Continuity and smoothness

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Xing-Gang He, Chun-Tai Liu

* Xing-Gang He*, Department of Mathematics, Central China Normal University, Wuhan, 430079, P. R. China, e-mail: ` xingganghe@sina.com`; * Chun-Tai Liu*, Department of Mathematics, Central China Normal University, Wuhan, 430079, P. R. China, e-mail: ` lct984@163.com`

**Abstract:** In this paper we give some criteria for the existence of compactly supported $C^{k+\al}$-solutions ($k$ is an integer and $0\le\al<1$) of matrix refinement equations. Several examples are presented to illustrate the general theory.

**Keywords:** matrix refinement equation, continuity, smoothness, iteration, multi-wavelet

**Classification (MSC 2000):** 39B42, 39B12, 42C40

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