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Orthogonal Polynomials on S-Curves Associated with Genus One Surfaces

Indiana University-Purdue University Indianapolis (IUPUI) / 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.

Identiferoai:union.ndltd.org:IUPUI/oai:scholarworks.iupui.edu:1805/23029
Date08 1900
CreatorsBarhoumi, Ahmad
ContributorsYattselev, Maxim, Bleher, Pavel, Its, Alexander, Tarasov, Vitaly
Source SetsIndiana University-Purdue University Indianapolis
Languageen_US
Detected LanguageEnglish
TypeThesis

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