Browsing by Subject "Equilibrium measure"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Open Access Asymptotics of extremal polynomials for some special cases(Bilkent University, 2017-05) Alpan, GökalpWe 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 RItem Open Access Orthogonal Polynomials Associated with Equilibrium Measures on ℝ(Springer Netherlands, 2017) Alpan, GökalpLet K be a non-polar compact subset of ℝ and μK denote the equilibrium measure of K. Furthermore, let Pn(⋅;μK) be the n-th monic orthogonal polynomial for μK. It is shown that ∥Pn(⋅;μK)∥L2(μK), the Hilbert norm of Pn(⋅;μK) in L2(μK), is bounded below by Cap(K)n for each n∈ ℕ. A sufficient condition is given for(∥Pn(⋅;μK)∥L2(μK)/Cap(K)n)n=1∞ to be unbounded. More detailed results are presented for sets which are union of finitely many intervals. © 2016, Springer Science+Business Media Dordrecht.