Analytic continuation of fractal functions
by Professor Michael Barnsley
Abstract: Analytic continuation is a central concept in mathematics. For example, Riemannian geometry emerged from the continuation of real analytic functions to the complex realm. In this talk, designed for a general mathematical audience, I will describe a remarkable generalization of analytic continuation to include analytic fractal functions. (An analytic fractal function is defined by the property that its graph is the attractor of an analytic iterated function systems. Analytic fractal functions include real analytic functions, Takagi curves, Kieswetter curves, Koch curves, and fractal interpolation functions; Daubechies wavelets are piecewise analytic fractal functions.) I will describe the method of continuation, outline the proof of a key uniqueness theorem, and give some examples."