Mikhail Konstantinovich Potapov

Abstract

The well-known mathematician in the theory of functions of a real variable and a leading expert in mathematical education Mikhail Konstantinovich Potapov observed his 90th birthday on 29 January 2021. Potapov was born in Pyatigorsk and graduated from Pyatigorsk Pedagogical Institute in 1952 as a teacher of mathematics and physics in secondary school. Subsequently, after he developed into a prominent figure in mathematics, he remained always mindful of the teaching of mathematics in school and he wrote innovative textbooks. He completed his postgraduate studies in the Faculty of Mechanics and Mathematics at Moscow State University (MSU), with S. M. Nikol’skii as his scientific advisor. Since then Potapov’s research and teaching activities have been connected with MSU, where he has been one of the leading professors in the Faculty of Mechanics and Mathematics for decades. He is the author of more than 250 research papers, and the total number of his publications exceeds 800. The main topics of his investigations are the theory of approximations of functions, embedding theorems, and trigonometric series. He was one of the first authors to study approximations of functions by algebraic polynomials in an integral metric. In the 1950s he proved Jackson’s theorem for Lipschitz classes in the spaces Lp, 1 ⩽ p < ∞. He described various structural characteristics of classes of continuous functions on a closed interval or a half-line that have one or another order of best approximation by algebraic polynomials, and he answered the question of the stability of these characteristics in the classical cases of Jacobi and Laguerre weights. He proved Jackson’s theorem and its converse for best approximation by algebraic polynomials and the moduli of smoothness defined in terms of symmetric