%0 Thesis %A Barhoumi, Ahmad Bassam %D 2020 %T ORTHOGONAL POLYNOMIALS ON S-CURVES ASSOCIATED WITH GENUS ONE SURFACES %U https://hammer.purdue.edu/articles/thesis/ORTHOGONAL_POLYNOMIALS_ON_S-CURVES_ASSOCIATED_WITH_GENUS_ONE_SURFACES/12470084 %R 10.25394/PGS.12470084.v1 %2 https://hammer.purdue.edu/ndownloader/files/23094356 %K Orthogonal Polynomials %K Padé approximants %K Riemann–Hilbert problem %K Mathematical Physics not elsewhere classified %K Approximation Theory and Asymptotic Methods %X We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration we will focus on measures of the form d\mu(z) = \rho(z) dz where the function \rho may depend on other auxiliary parameters. Much of the asymptotic analysis is done via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method, and relies heavily on notions from logarithmic potential theory. %I Purdue University Graduate School