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ORTHOGONAL POLYNOMIALS ON S-CURVES ASSOCIATED WITH GENUS ONE SURFACES

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thesis
posted on 16.06.2020 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.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

Indianapolis

Advisor/Supervisor/Committee Chair

Maxim Yattselev

Additional Committee Member 2

Pavel Bleher

Additional Committee Member 3

Alexander Its

Additional Committee Member 4

Vitaly Tarasov

Licence

Exports