RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 Video Library Archive Most viewed videos Search RSS New in collection

You may need the following programs to see the files

Ìemorial conference dedicated to the memory of Ivan Matveevich Vinogradov
March 28, 2019 14:30–14:55, Moscow, Steklov Mathematical Institute, Conference hall

Orthorecursive expansion of unity

A. B. Kalmyninab

a Department of Mathematics, National Research University "Higher School of Economics", Moscow
b International laboratory for Mirror Symmetry and Automorphic Forms, National Research University "Higher School of Economics" (HSE), Moscow
 Video records: MP4 393.6 Mb

Abstract: Define the sequence $c_n$ by relations
$$c_0=1, \quad \frac{c_0}{n+1} + \ldots + \frac{c_n}{2n+1} = 0$$
for all $n>0$. Despite simple definition, this sequence has interesting properties and turns out to be connected with orthorecursive expansions in the space $L^{2}[0,1]$. In my talk, I will discuss these properties (some of them are proved and some are observed experimentally) and tell you how permutations of the set of $n$ elements help us to prove that $c_n\neq 0$.