级联算法在Besov和Triebel-Lizorkin空间上的有界性和收敛性(II)

摘要

In this part, we shall characterize completely convergence and increment of the cascade algorithm in Besov spaces and Triebel-Lizorkin spaces by joint spectral radius on certain finitely dimensional space, give a new proof of moment conditions for the initial distribution and the refinable distribution in the cascade algorithm, establish close relationship between regularity of the refinable distribution and convergence and boundedness of the cascade algorithm, and apply the characterization to the existence of compactly supported solutions of nonhomogeneous refinement equations. From our results, we see that the initial and the refinable distribution of the cascade algorithm satisfyless moment conditions for the boundedness of the cascade algorithm than for the convergence of the cascade algorithm, and for 0<1 than for p1. It is observed that the convergence and boundedness of the cascade algorithm are equivalent to each other under certain restriction on the indices of regularity of function space and the rate of convergence of the cascade algorithm, and certain assumptions on the refinable distribution.%本文利用联合谱半径刻画了级联算法在Besov和Triebel-Lizorkin 空间上的收敛性, 给出了级联算法初值函数矩条件的新证明, 并利用到细分分布的光滑性和非齐次细分方程解的存在性等方面. 特别地, 在某些条件下，我们证明了级联算法的有界性和收敛性相互等价.