Journal article
Fourier frequencies in affine iterated function systems
Journal of functional analysis, Vol.247(1), pp.110-137
2007
DOI: 10.1016/j.jfa.2007.03.002
Abstract
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in R d , and the “IFS” refers to such a finite system of transformations, or functions. The iteration limits are pairs ( X , μ ) where X is a compact subset of R d (the support of μ), and the measure μ is a probability measure determined uniquely by the initial IFS mappings, and a certain strong invariance axiom. The two questions we study are: (1) existence of an orthogonal Fourier basis in the Hilbert space L 2 ( X , μ ) ; and (2) explicit constructions of Fourier bases from the given data defining the IFS.
Details
- Title: Subtitle
- Fourier frequencies in affine iterated function systems
- Creators
- Dorin Ervin Dutkay - Department of Mathematics, University of Central Florida, 4000 Central Florida Blvd., PO box 161364, Orlando, FL 32816-1364, USAPalle E.T Jorgensen - Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.247(1), pp.110-137
- DOI
- 10.1016/j.jfa.2007.03.002
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2007
- Academic Unit
- Mathematics
- Record Identifier
- 9983985852002771
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