Subdivision schemes with polynomially decaying masks
The \(L_2\)-solutions of vector refinement equations with polynomially decaying masks and a general dilation matrix, which plays a vital role for characterizations of wavelets and biorthogonal wavelets with infinite support are studied here [cf. \textit{B. Han} and \textit{R.-Q. Jia}, Appl. Comput. Harmon. Anal. 23, 321--345 (2007; Zbl 1141.42023)]. Some basic properties the cascade operator and the transition operator are shown. A necessary and sufficient condition for the convergence of certain subdivision schemes has also been given.
scientific article; zbMATH DE number 5694696
scientific article