Orthogonal Exponentials for Bernoulli Iterated Function Systems
We investigate certain spectral properties of the Bernoulli convolution measures on attractor sets arising from iterated function systems (IFSs) on ℝ. 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 λ = 3/4 in which the IFS has overlap. We also determine rational λ = a/b for which infinite sets of orthogonal exponentials exist.
KeywordsHilbert Space Nonzero Element Invariance Property Iterate Function System Pisot Number
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