Exposition of the lectures by S. B. Stechkin on approximation theory

Abstract

Professor Sergey Borisovich Stechkin (1920–1995) was a famous Russian mathematician working in the theory of approximation and the theory of numbers. He was also an exceptional personality and a brilliant lecturer who for many years gave deep sophisticated courses on approximation theory at the M.V. Lomonosov Moscow State University and at the Ural State University. Stechkin was a supervisor of many students who themselves became well-known experts in the theory of approximation. In 2010, several of his former post-graduate students, now distinguished professors, prepared an upgraded version of the record of Stechkin’s lectures given in 1970–1971. Exposition of Stechkin’s lectures, published in Russian in 2010 by the Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, immediately became popular. Without doubt, the English translation of the Lectures would be of great interest for the international community of analysts working in the theory of approximation. This opinion was enthusiastically shared by the Editorial Board of the Eurasian Mathematical Journal and it was decided to publish the translation as one of the issues of this journal. During translation some additional editing of the original text was done. In particular, the list of references was essentially enlarged, and references were given to most of the statements mentioned in the lecture course without proofs.