Optimal approximation order and optimal smoothnessof a multivariate dual scaling functions
Li Cui · 2002
A biorthogonal wavelet is derived from a multiresolution analysis generated by a pair consisting of a scaling function and its dual scaling function.It is well known that high smoothness,small support,and high vanishing moments are the three most important features of a biorthogonal wavelet.In this paper,the relations among these three properties are discussed and the optimal approximation order and optimal smoothness of a multivariate dual scaling functions are obtained.