Wavelet constructions in non-linear dynamics

Authors:
Dorin Ervin Dutkay and Palle E.T. Jorgensen

Journal:
Electron. Res. Announc. Amer. Math. Soc. **11** (2005), 21-33

MSC (2000):
Primary 60G18; Secondary 42C40, 46G15, 42A65, 28A50, 30D05, 47D07, 37F20

Published electronically:
March 7, 2005

MathSciNet review:
2122446

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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Additional Information

**Dorin Ervin Dutkay**

Affiliation:
Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419

Email:
ddutkay@math.rutgers.edu

**Palle E.T. Jorgensen**

Affiliation:
Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419

Email:
jorgen@math.uiowa.edu

DOI:
https://doi.org/10.1090/S1079-6762-05-00143-5

Keywords:
Measures,
projective limits,
transfer operator,
martingale,
fixed point,
multiresolution,
Julia set,
subshift,
wavelet

Received by editor(s):
October 28, 2004

Published electronically:
March 7, 2005

Communicated by:
Boris Hasselblatt

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.