Nonlinear operator related to refinable function vectors

Ying Huang; Bruce W. Suter

doi:10.1117/12.255290

23 October 1996 Nonlinear operator related to refinable function vectors

Ying Huang, Bruce W. Suter

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255290
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

We study a certain nonlinear operator T from L²(R, C^N) to itself under which every refinable function vector is a fixed point. The iterations Tⁿf of T on any f (epsilon) L²(R, C^N) 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.

Citation Download Citation

Ying Huang and Bruce W. Suter "Nonlinear operator related to refinable function vectors", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255290

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