Title

Fourier Frequencies In Affine Iterated Function Systems

Keywords

Affine fractal; Attractor; Fourier series; Hilbert space; Spectral measure; Spectrum

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 Rd, 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 Rd (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 L2 (X, μ); and (2) explicit constructions of Fourier bases from the given data defining the IFS. © 2007 Elsevier Inc. All rights reserved.

Publication Date

6-1-2007

Publication Title

Journal of Functional Analysis

Volume

247

Issue

1

Number of Pages

110-137

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2007.03.002

Socpus ID

34247247656 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34247247656

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