Some Open Problems Concerning Orthogonal Polynomials on Fractals and Related Questions

We discuss several open problems related to analysis on fractals: estimates of the Green functions, the growth rates of the Markov factors with respect to the extension property of compact sets, asymptotics of orthogonal polynomials and the Parreau-Widom condition, Hausdorff measures and the Hausdorff dimension of the equilibrium measure on generalized Julia sets.