Riemann-Hilbert methods in the theory of orthogonal polynomials. (English) Zbl 1134.42325
Gesztesy, Fritz (ed.) et al., Spectral theory and mathematical physics. A festschrift in honor of Barry Simon’s 60th birthday. Ergodic Schrödinger operators, singular spectrum, orthogonal polynomials, and inverse spectral theory. Based on the SimonFest conference, Pasadena, CA, USA, March 27–31, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4249-2/pt.2; 978-0-8218-3783-2/set). Proceedings of Symposia in Pure Mathematics 76, Pt. 2, 715-740 (2007).
Summary: We describe various applications of the Riemann-Hilbert method to the theory of orthogonal polynomials on the line and on the circle.
For the entire collection see [Zbl 1110.00015].
For the entire collection see [Zbl 1110.00015].
MSC:
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 30E05 | Moment problems and interpolation problems in the complex plane |
| 30E20 | Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
