Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I

Journal Article (Journal Article)

Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert 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 Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method. © 2008 Springer Science+Business Media B.V.

Full Text

Duke Authors

Cited Authors

  • McLaughlin, KTR; Vartanian, AH; Zhou, X

Published Date

  • November 1, 2008

Published In

Volume / Issue

  • 11 / 3-4

Start / End Page

  • 187 - 364

International Standard Serial Number (ISSN)

  • 1385-0172

Digital Object Identifier (DOI)

  • 10.1007/s11040-008-9042-y

Citation Source

  • Scopus