Orthogonal Exponentials for Bernoulli Iterated Function Systems

Details Orthogonal Exponentials for Bernoulli Iterated Function Systems Orthogonal Exponentials for Bernoulli Iterated Function Systems

2007-03-13

arxiv.org/abs/math/0703385v1

Current Trends in Harmonic Analysis and Its Applications: Wavelets and Frames Workshop in Honor of Larry Baggett, Birkhauser,

Mathematics

Operator Algebras

Scientific paper

We investigate certain spectral properties of the Bernoulli convolution measures on attractor sets arising from iterated function systems on the real line. In particular, we examine collections of orthogonal exponential functions in the Hilbert space of square integrable functions on the attractor. We carefully examine a test case where the parameter lambda is equal to 3/4 and therefore the IFS has overlap. We also determine rational values of lambda for which infinite sets of orthogonal exponentials exist.

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