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:purdue.edu/oai:figshare.com:article/12470084 |
| Date | 16 June 2020 |
| Creators | Ahmad Bassam Barhoumi (8964155) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/ORTHOGONAL_POLYNOMIALS_ON_S-CURVES_ASSOCIATED_WITH_GENUS_ONE_SURFACES/12470084 |
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