Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 747-762, 2007

Matrix refinement equations:
Continuity and smoothness

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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