Abstract:
V.S. Videnskii – world famous expert in the approximation theory, author of 116 publications, including two small monographs, the last student of one of the greatest mathematicians of the 20th century, S.N. Bernstein. V.S. Videnskii was born in Berdichev, graduated from Moscow State University (1947), made his postgraduate studies there (1950). From 1947 to 1962 he was a junior assistant researcher to Academician S.N. Bernstein at V.A. Steklov Mathematical Institute. In 1962 he moved to Leningrad where he worked as a professor at Leningrad State Institute of Communications named after prof. M.A. Bonch-Bruevich. Since 1967 he was the head, and from 1978 until 2015 a professor at the Department of Mathematical Analysis in the Leningrad State Pedagogical Institute (now RSPU) named after A.I. Herzen. V.S. Videnskii solved two famous problems of I.I. Privalov (1919) and D. Jackson (1931) on an extremal estimate for the derivative of a trigonometric polynomial on a segment less than the period; obtained an analogue of Chebyshev's alternance theorem, namely, he gave a complete description of the arguments with which the best approximation of a continuous function by algebraic polynomials in the complex plane is achieved; obtained an exact description of the Taylor coefficients of an even entire function of genus zero; established inequalities between convex functions and entire functions, applying those inequalities to the theory of approximation with weight on the real line and for solving a problem that arose in the theory of Orlicz spaces; constructed an analogue of Bernstein polynomials for products of Cauchy kernels; built modifications of Bernstein polynomials, which converge the faster, the more derivatives the function has; proved two theorems about one fourth, significantly refining the theorems of P.P. Korovkin and V.G. Amelkovich. Once V.S. Videnskii tackled a topic, he investigated it exhaustively without leaving any open questions.
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