Alpan, Gökalp2017-06-082017-06-082017-052017-052017-05-07http://hdl.handle.net/11693/33196Cataloged from PDF version of article.Thesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2017.Includes bibliographical references (leaves 129-141).We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uck-B uger 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 Hausdor 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 su cient condition for this sequence to be unbounded above. We suggest de nitions for the Szeg}o class and the isospectral torus for a generic subset of Rix, 141 pages ; 30 cmEnglishinfo:eu-repo/semantics/openAccessOrthogonal polynomialsChebyshev polynomialsCantor setsSzegö classIsospectral torusWidom factorsParreau-Widom setsGreen functionHausdorff measureEquilibrium measureAlmost periodicityThesisB155696