[0,1]区间上的r重正交多小波基

Orthonormal Multi-Wavelets on the Interval [0,1] with Multiptiplicity r

本文利用L2（R）上的紧支撑正交的多尺度函数和多小波构造出有限区间[0,1]上的正交多尺度函数及相应的正交多小波.本文构造的逼近空间Vj[0,1]与相应的小波子空间Wj[0,1]具有维数相同的特点,从而给它的应用带来巨大方便.最后给出重数为2时的[0,1]区间上的正交多小波基构造算例.

The objective of this paper is to exhibit the construction of compactly supported orthonormal multi-scaling functions and the corresponding compactly supported orthonormal multi-wevelets on the interval [0,1] with multiplicity r, using compactly supported orthonormal multi-scaling functions and the corresponding supported orthonormal multi-wavelets on L2(R). Since Dim Vj[0,1] = DimWj[0, 1] ( j≤j0), the multi-wavelets are more convenient in its application. The corresponding example is given.