Bazı özel durumlar için aşıt polinomların asimptotikleri

We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Brück-Büger and weakly equilibrium Cantor sets which was introduced in [62]. We give characterizations for Parreau-Widom condition and optimal smoothness of the Green function for the weakly equilibrium Cantor sets. We also show that, for small parameters, the corresponding Hausdorff measure and the equilibrium measure of a set from this family are mutually absolutely continuous. We prove that the sequence of Widom-Hilbert factors for the equilibrium measure of a non-polar compact subset of R is bounded below by 1. We give a sufficient condition for this sequence to be unbounded above. We suggest definitions for the Szegö class and the isospectral torus for a generic subset of R.