Fourier frequencies in affine iterated function systems
Abbreviated Journal Title
J. Funct. Anal.
fourier series; affine fractal; spectrum; spectral measure; Hilbert; space; attractor; HARMONIC-ANALYSIS; SPECTRAL THEORY; CANTOR MEASURES; SETS; FRACTALS; DIMENSIONS; OPERATORS; SERIES; TILES; Mathematics
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, mu) where X is a compact subset of R-d (the support of mu), and the measure mu 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, mu); and (2) explicit constructions of Fourier bases from the given data defining the IFS. (C) 2007 Elsevier Inc. All rights reserved.
Journal of Functional Analysis
"Fourier frequencies in affine iterated function systems" (2007). Faculty Bibliography 2000s. 7081.