Nikol’skii, Sergei Mikhailovich
Born Apr. 17 (30), 1905, at the Talitsa Factory in Perm’ Province, now the city of Talitsa, Sverdlovsk Oblast. Soviet mathematician. Academician of the Academy of Sciences of the USSR (1972; corresponding member, 1968). Member of the CPSU since 1952.
Nikol’skii graduated from the Ekaterinoslav Institute of Public Education (now the University of Dnepropetrovsk) in 1929 and worked there from 1930 to 1940. In 1940 he began working at the V. A. Steklov Institute of Mathematics of the Academy of Sciences of the USSR, and in 1947 he became a professor at the Moscow Physicotechnical Institute.
Nikol’skii’s work deals mostly with functional analysis, the theory of approximation of functions, the theory of imbedding of classes of differentiable functions of many variables, direct methods of the calculus of variations, and the theory of boundary-value problems for partial differential equations. His studies on approximation theory are of great importance. He found asymptotically exact estimates for approximation of functions by trigonometric and algebraic polynomials. He developed a theory of optimal quadrature formulas. Nikol’skii developed methods of approximation by entire exponential-type functions that enabled him to derive direct and inverse imbedding theorems for generalized Holder classes of functions of many variables. He also provided new formulations of boundary-value problems for higher-order elliptic equations with strong degeneracy at the boundary and investigated these formulations by a variational method. Nikol’skii received the State Prize of the USSR in 1952 and the P. L. Chebyshev Prize in 1972. He has been awarded the Order of the Red Banner of Labor and several medals.
WORKSKvadraturnye formuly. Moscow, 1958.
Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniia. Moscow, 1969.
Kurs matematicheskogo analiza, vols. 1–2. Moscow, 1973.
REFERENCEUspekhi matematicheskikh nauk, 1956, vol. 11, fase. 2, pp. 239–46; 1965, vol. 20, fase. 5, pp. 275–87.
P. I. LIZORKIN