用非线性算子研究可细化函数向量

Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96) Pub Date : 1996-06-18 DOI:10.1109/TFSA.1996.547472

Ying Huang, B. Suter

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引用次数: 0

摘要

研究了一类非线性算子T从L/sup 2/(R,C/sup N/)到其自身，其中每个可细化函数向量都是不动点。研究了T在任意f/spl isin/L/sup 2/(R,C/sup n/)上具有Riesz基性质的迭代T/sup n/f;它们是“级联算法”，f的迭代权只依赖于f。文中还给出了T/sup m/f在不同拓扑下收敛到极限的条件。

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A study of refinable function vectors via a nonlinear operator

This paper studies a certain nonlinear operator T from L/sup 2/(R,C/sup N/) to itself under which every refinable function vector is a fixed point. The iterations T/sup n/f of T on any f/spl isin/L/sup 2/(R,C/sup 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 T/sup m/f to a limit in different topologies.

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Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)

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