Computational Methods and Function Theory

, Volume 11, Issue 1, pp 161–178 | Cite as

The Global Parametrix in the Riemann-Hilbert Steepest Descent Analysis for Orthogonal Polynomials



In the application of the Deift-Zhou steepest descent method to the Riemann-Hilbert problem for orthogonal polynomials, a model Riemann-Hilbert problem that appears in the multi-cut case is solved with the use of hyperelliptic theta functions. We present here an alternative approach which uses meromorphic differentials instead of theta functions to construct the solution of the model Riemann-Hilbert problem. By using this representation, we obtain a new and elementary proof for the solvability of the model Riemann-Hilbert problem.


Riemann-Hilbert problem meromorphic differentials solvability 

2000 MSC

34M50 30F30 


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Copyright information

© Heldermann  Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Department of MathematicsUniversity of BristolBristolUK

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