Wavelet constructions in non-linear dynamics

2005/01/10 by Dorin Ervin Dutkay, Palle E. T. Jorgensen · 1 citation
Mathematics · #math.DS #math.FA #msc:60G18 #msc:42C40 #msc:46G15 #msc:42A65 #msc:28A50 #msc:30D05 #msc:47D07 #msc:37F20

paper · pdf

published as Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 21-33 · 13 pages, LaTeX2e "amsart" document class

arxiv created 2005/01/10 · arxiv updated 2009/12/01

Abstract

We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L²-martingales which have wavelet bases.

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