Subdivision schemes and refinement equations with nonnegative masks

JOURNAL OF APPROXIMATION THEORY

卷:113

Article

Wang, Y

关键词: nonnegative mask;    cascade algorithm;    subdivision scheme;    refinement equation;    refutable function;   

DOI  :  10.1006/jath.2001.3623

来源: Elsevier

【 摘 要 】

We consider the two-scale refinement equation f(x) = Sigma(n=0)(N) c(n)f(2x - n) with Sigma(n) c(2n) = Sigma(n)c(2n+1) = 1 where c(0), c(N) not equal 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all c(n) greater than or equal to 0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 0 < c(0), c(N) < 1 and the greatest common divisor of S = {n: c(n) > 0} is 1. We prove the conjecture for a large class of refinement equations. (C) 2001 Academic Press.

【 授权许可】

Free