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- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Heldermann Verlag
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/BF03321795
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Aug 20, 2010