A new class of multi-wavelet bases: V-system
A new class of multi-wavelet bases: V-system
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DOI：
10.1007/s10114-012-9424-8
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
Chao Huang;L. Yang;D. Qi
中科院分区：
文献类型：
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作者：
Chao Huang;L. Yang;D. Qi
v系是定义在区间[0,1]上的函数的完备正交系统，由有限个Legendre多项式和函数发生器的展开和平移生成，由有限个连续和不连续函数组成。v系具有正交性、对称性、完备性和短紧支撑等有趣的性质。本文证明了v系本质上是一个特殊的多小波基。结果，通过完善的多小波理论，建立了v系的一些基本性质。从这个角度出发，可以构造更多其他的v系统。
The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.