Use of operator algebras in the analysis of measures from wavelets and iterated function systems
نویسنده
چکیده
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras. Let (X, d) be a compact metric space, and let an iterated function system (IFS) be given on X, i.e., a finite set of continuous maps σi: X → X, i = 0, 1, · · · , N −1. The maps σi transform the measures μ on X into new measures μi. If the diameter of σi1 ◦· · ·◦σik (X) tends to zero as k → ∞, and if pi > 0 satisfies ∑ i pi = 1, then it is known that there is a unique Borel probability measure μ on X such that
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