Two Courses on Orthogonal Polynomials and Special Functions

Departamento de Matemática, Universidade de Coimbra

  3-5 July 2001

With support from CMUC (Centro de Matemática da Universidade de Coimbra)and Socrates programme

Schedule of the course

Abstracts

Author: Alexander Aptekarev

Title: Scalar and Matrix Riemann Problem approach to the
asymptotics of polynomials orthogonal with respect to a
complex weight.

Abstract:

1. Cauchy integral theorem and solution of the jump problem.
   
2. Short introduction to Riemann surfaces, meromorphic differentials.
   
3. Cauchy Integral theorem on the Riemann surfaces and solution of Boumdary Value Problems.
   
4. Scalar Riemann problem approach of J.Nuttall to the asymptotics of complex orthogonal polynomials.
   
5. Matrix Riemann problem approach of P.Deift to the asymptotics of complex orthogonal polynomials.

The course will cover the main properties of the logarithmic potential up to the proof of the existence of the equilibrium measure. Applications of this theory to asymptotics of orthogonal polynomials and convergence of interpolatory processes in rational approximation will be seen.

• Amilcar Branquinho (Departamento de Matemática Universidade de Coimbra)

• Ana Foulquié (Departamento de Matemática Universidade de Aveiro) 

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