Characterization of Continuous, Four-Coefficient Scaling Functions via Matrix Spectral Radius
Characterization of Continuous, Four-Coefficient Scaling Functions via Matrix Spectral Radius
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DOI：
10.1137/s0895479897323750
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发表时间：
2000-04
期刊：
影响因子：
--
通讯作者：
Markus Bröker;Xinlong Zhou
中科院分区：
文献类型：
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作者：
Markus Bröker;Xinlong Zhou
利用矩阵的谱半径刻画了一类四系数膨胀方程连续解的存在性。这种解存在的标准可以很快得到检验。结果对Colella和Heil在1992年提出的一个猜想给出了肯定的回答。此外，利用我们的标准，我们找到了最光滑的紧支撑四系数正交尺度函数，从而最光滑的紧支撑正交小波产生的尺度函数。
We characterize the existence of continuous solutions of a four-coefficient dilation equation in terms of the usual spectral radius of a matrix. The criteria for the existence of such a solution can be very quickly examined. As a result we give an affirmative answer to a conjecture raised by Colella and Heil in 1992. Moreover, using our criteria we find the smoothest compactly supported four-coefficient orthogonal scaling function and thus the smoothest compactly supported orthonormal wavelet generated by this scaling function.