The Padé approximant is the best approximant of a given power series by a rational function of a given order. Padé approximants are closely related to orthogonal polynomials and Chebyshev (functional) continued fractions. The purpose of the course is to introduce students to the basics of the classical Stahl theory of the convergence of Padé approximants and to the modern view on this theory. Also, within the framework of the course, we suppose to show how elements of the Stahl theory can be applied to the study of the asymptotic properties of such generalizations of Padé approximants as multipoint Padé approximants, Hermite–Padé polynomials, Schafer approximants. We plan to state some open problems of the theory of rational approximations.

Lecturers
Komlov Aleksandr Vladimirovich
Suetin Sergey Pavlovich

Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center