Orthogonal Exponentials for Bernoulli Iterated Function Systems

Abstract

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.