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Wavelet constructions in non-linear dynamics

Author(s): Dorin Ervin Dutkay; 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
Posted: March 7, 2005
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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 $L^2$-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: 10.1090/S1079-6762-05-00143-5
PII: S 1079-6762(05)00143-5
Keywords: Measures, projective limits, transfer operator, martingale, fixed point, multiresolution, Julia set, subshift, wavelet
Received by editor(s): October 28, 2004
Posted: March 7, 2005
Communicated by: Boris Hasselblatt
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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