P L Ul'yanov, Reminiscences about Sergei Borisovich Stechkin

Pyotr Lavrentyevich Ul'yanov (1928-2006) graduated from Saratov State University in 1950, then studied at Moscow State University, where he received his Candidate of Sciences degree in 1953 advised by Nina Bari. He continued to work at Moscow State University and, from 1957, he also worked at the Steklov Institute of Mathematics. He was awarded his doctorate (equivalent to the habilitation) in 1960 at Moscow State University. Appointed as a professor there, in 1979 he became head of the Department of Function Theory and Functional Analysis.

We give some extracts from the paper P L Ul'yanov, Reminiscences about Sergei Borisovich Stechkin, Russian Math. Surveys 51 (6) (1996), 1015-1024.

Reminiscences about Sergei Borisovich Stechkin

Sergei Borisovich Stechkin was born in Moscow on 6 September 1920 and died in Moscow on 22 November 1995.

1. Stechkin was an eminent mathematician. He carried out research in the theory of trigonometric and orthogonal series, the approximation of functions by algebraic and trigonometric polynomials, the approximation of functions by splines, approximation in Banach spaces, the approximation of operators, and several areas in number theory.

Stechkin was an outstanding teacher and lecturer. In the Mechanics and Mathematics Faculty of Moscow State University (MGU) he was one of the best lecturers on mathematical analysis and specialised courses. His seminar on the theory of functions was well known. He created a leading school, in which his students actively participated, and some fifteen of them defended their D.Sc. dissertations. Stechkin was a founder of the Mathematics and Mechanics Institute of the Urals Section of the USSR Academy of Sciences at Sverdlovsk (1955-1967).

From its inception in 1967 until his death, Stechkin was a member of the Editorial Board of Matematicheskie Zametki (Mathematical Notes) and editor-in-chief of the journal during its first 20 years.

Sergei Borisovich Stechkin played a large part in the development of the theory of functions in the Soviet Union. This was touched on above. But it must also be noted that he often delivered lectures and reports at various institutions and conferences, at which he described his own results, and also indicated those directions in function theory in which more active work would be necessary. He often refereed articles for journals and reviewed dissertations from the USSR Higher Degrees Commission. These reports were by no means always favourable. His phenomenal activity as a member of the council for the examination of D.Sc. and Ph.D. dissertations on function theory at the Steklov Institute of Mathematics and at Moscow State University is well known. Stechkin was intolerant of any foolishness or lack of education shown by people in his specialised field and sometimes expressed his opinion on this subject sharply. He himself had an encyclopaedic knowledge of the theory of functions and many people went to him seeking advice and references in the literature.

Stechkin was interested in several areas of function theory. In this note we shall only deal with some questions he investigated in the theory of trigonometric and orthogonal series. We shall recount their subsequent development and formulate some unsolved problems in this field.

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2. I became acquainted with Stechkin at the end of 1950 at D E Men'shov and N K Bari's seminar "Theory of functions of a real variable" at Moscow State University. In September 1950 I had been accepted as a research student there and began to attend this seminar. At first I understood but little in the lectures, since they were delivered rather quickly and were on topics already familiar to the participants. The speakers were often A S Kronrod and his students (Ε Μ Landis, A G Vitushkin, R A Minlos, and others). But then Stechkin spoke "On the convergence and divergence of trigonometric series", and his lecture I understood perfectly. This talk was also delivered at a meeting of the Moscow Mathematical Society on 19 December 1950 and published in his paper [On the convergence and divergence of trigonometric series (1951)].

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3. Stechkin obtained his first results on the absolute convergence of orthogonal series during his years as a research student. He gave a report about this work to the Moscow Mathematical Society on 17 December 1946 and published it in the paper [On the absolute convergence of orthogonal series (1947)].

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4. Sergei Borisovich Stechkin and I had known one another from 1950 until his death in 1995. We worked together in the department of function theory at the Steklov Institute of Mathematics and in the Faculty of Mechanics and Mathematics at Moscow State University. Initially Stechkin worked at Moscow State University in the department of function theory and functional analysis, but then transferred to the department of mathematical analysis, because he regularly gave the mathematical analysis course there. The journal Matematicheskie Zametki (Mathematical Notes) has appeared since 1967 and for many years I was deputy editor-in-chief, Stechkin being editor-in-chief. At that time the journal was one of the leading mathematical periodicals in the USSR.

From 1957 to 1967 Stechkin worked in the Mathematics and Mechanics Institute of the Urals Section of the USSR Academy of Sciences. During that time he and I wrote two papers [S B Stechkin and P L Ul'yanov, On sets of uniqueness (1962)] and [S B Stechkin and P L Ul'yanov, Subsequences of convergence of series (1965)], meeting periodically in Moscow and in Sverdlovsk.

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