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.
| Identifer | oai:union.ndltd.org:IUPUI/oai:scholarworks.iupui.edu:1805/23029 |
| Date | 08 1900 |
| Creators | Barhoumi, Ahmad |
| Contributors | Yattselev, Maxim, Bleher, Pavel, Its, Alexander, Tarasov, Vitaly |
| Source Sets | Indiana University-Purdue University Indianapolis |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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