Nonlinear operator related to refinable function vectors
Ying J. Huang, Bruce W. Suter · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
We study a certain nonlinear operator T from L2(R, CN) to itself under which every refinable function vector is a fixed point. The iterations Tnf of T on any f (epsilon) L2(R, CN) with the Riesz basis property are investigated; they turn out to be the 'cascade algorithm' iterates of f with weights depending on f only. The paper also gives conditions for convergence of Tnf to a limit in different topologies.