Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some different...Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli＇s work.展开更多
基金Supported by National Natural Science Foundation of China （Crant No. 10871012） and Natural Science Foundation of Beijing （Grant No. 1082003）
文摘Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli＇s work.
