Видеотека: A. V. Komlov, Constructive reconstruction of values of an algebraic function via polynomial Hermite--Padé $m$-system

ВИДЕОТЕКА


Дни анализа в Сириусе 26 октября 2021 г. 10:00, г. Сочи, online via Zoom at 09:00 CEST (=08:00 BST, =03:00 EDT)

Constructive reconstruction of values of an algebraic function via polynomial Hermite–Padé $m$-system A. V. Komlov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Аннотация: Let $f_0$ be a given germ of some algebraic function $f$ of degree $m+1$. We consider the following problem: how to reconstruct constructively the values of f in “as large a region as possible” on its Riemann surface $\mathfrak R$? We introduce the polynomial Hermite–Padé $m$-system, which, in our case, is constructed from the tuple of the germs $[1, f_0,f_0^2,\dots,f_0^m]$. This system includes the Hermite–Padé polynomials of the first and of the second type. We show how to reconstruct the values of $f$ on the first $m$ sheets of the so-called Nuttall partition of the Riemann surface $\mathfrak R$ via the polynomial Hermite–Padé $m$-system. Язык доклада: английский Website: https://us02web.zoom.us/j/6250951776?pwd=aG5YNkJndWIxaGZoQlBxbWFOWHA3UT09 ^* ID: 625 095 1776, password: pade