Video Library
Most viewed videos

New in collection

You may need the following programs to see the files

Conference in honor of Guillermo Lуpez Lagomasino's 60th birthday "International Workshop on Orthogonal Polynomials and Approximation Theory" IWOPA'08
September 9, 2008 09:30, Madrid

Hermite-Padé approximants for systems of Markov functions generated by cyclic

A. Aptekarevab

a Lomonosov Moscow State University
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
Video records:
Windows Media 228.2 Mb
Flash Video 411.1 Mb
MP4 411.1 Mb

Number of views:
This page:263
Video files:95

A. Aptekarev

Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: The Cauchy transform of a positive measure with the support on some interval of the real axis is called a Markov-type function. Systems of Markov functions are the basic models for understanding the analytic properties and the asymptotic behavior of the Hermite-Padé approximants. In 1980 E. M. Nikishin has put forward a special system of Markov functions with supports on the same interval which now is called the Nikishin system. It appears that this model system nicely reflects the general features of analytic functions (from the point of view of the Hermite-Padé approximants). Convergence of Hermite-Padé approximants for Nikishin system formed by two functions has been proven by Nikishin himself. The convergence result for Nikishin system formed by arbitrary number of functions has been proven by G. López Lagomasino and J. Bustamante in 1992. In 1997 A. Gonchar, E. Rakhmanov and V. Sorokin have introduced a notion of a generalized Nikishin system — a system of Markov functions generated by a graph-tree; they investigated also convergence and asymptotic properties of Hermite-Padé approximants for this system. In our lecture we discuss about further developments in this topic.

Language: English

SHARE: FaceBook Twitter Livejournal
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018