Math @ Duke

Publications [#244288] of Xin Zhou
Papers Published
 McLaughlin, KTR; Vartanian, AH; Zhou, X, Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I,
Mathematical Physics, Analysis and Geometry, vol. 11 no. 34
(November, 2008),
pp. 187364, Springer Nature, ISSN 13850172 [doi]
(last updated on 2021/11/27)
Abstract: Orthogonal rational functions are characterized in terms of a family of matrix RiemannHilbert problems on ℝ, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix RiemannHilbert problems which are amenable to asymptotic analysis via the DeiftZhou nonlinear steepestdescent method. © 2008 Springer Science+Business Media B.V.


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