A Sufficient and Necessary Condition for the Construction of Wavelets by Scaling Functions
Ding Xuan-hao · Gongcheng shuxue xuebao · 2007
Suppose that a multi-resolution analysis on L2(R) is produced by a scaling function g and Wo be a wavelet space. The method to construct a wavelet function h on W0 from the scaling function g is presented, and a sufficient and necessary condition for {h(x - k)} being a Riesz basis on W0 is proposed, then the decomposed relation of g and h introduced by Cheng for scaling sequences in l1 space is extended to scaling sequences in l2 space.