Orthogonal Polynomials on S-Curves Associated with Genus One Surfaces

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Date
2020-08
Language
American English
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Ph.D.
Degree Year
2020
Department
Mathematical Sciences
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Purdue University
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Abstract

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.

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Indiana University-Purdue University Indianapolis (IUPUI)
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