ar X iv : m at h / 06 04 54 7 v 2 [ m at h . FA ] 2 6 A pr 2 00 6 FOURIER FREQUENCIES IN AFFINE ITERATED FUNCTION SYSTEMS
نویسنده
چکیده
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) the interplay between the geometry of (X, µ) on the one side, and the spectral data entailed by possible Fourier bases.
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