ORTHOGONAL POLYNOMIALS ON S-CURVES ASSOCIATED WITH GENUS ONE SURFACES

2020-06-16T23:18:55Z (GMT) by Ahmad Bassam Barhoumi
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.