Sergei Bernstein
| Sergei Natanovich Bernstein | |
|---|---|
Sergei Natanovich Bernstein
|
|
| Born |
5 March 1880 Odessa, Kherson Governorate, Russian Empire |
| Died | 26 October 1968 (aged 88) Moscow, Soviet Union |
| Residence | Russian Empire, Soviet Union |
| Nationality | Soviet |
| Fields | Mathematics |
| Institutions |
University of Paris University of Goettingen University of Kharkiv Leningrad University Steklov Institute of Mathematics |
| Alma mater | University of Paris |
| Doctoral advisor |
Charles Émile Picard David Hilbert |
| Doctoral students |
Vladimir Brzhechka Yakov Geronimus Vasilii Goncharov Boris Rymarenko Sergey Stechkin |
| Known for |
Bernstein's inequality in analysis Bernstein inequalities in probability theory Bernstein polynomial Bernstein's theorem (approximation theory) Bernstein's theorem on monotone functions Bernstein problem in mathematical genetics |
Sergei Natanovich Bernstein (Russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as Bernshtein; 5 March 1880 – 26 October 1968) was a Russian and Soviet mathematician of Jewish origin known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory.
In his doctoral dissertation, submitted in 1904 to the Sorbonne, Bernstein solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations. His later work was devoted to Dirichlet's boundary problem for non-linear equations of elliptic type, where, in particular, he introduced a priori estimates.
In 1917, Bernstein suggested the first axiomatic foundation of probability theory, based on the underlying algebraic structure. It was later superseded by the measure-theoretic approach of Kolmogorov.
In the 1920s, he introduced a method for proving limit theorems for sums of dependent random variables.
Through his application of Bernstein polynomials, he laid the foundations of constructive function theory, a field studying the connection between smoothness properties of a function and its approximations by polynomials. In particular, he proved the Weierstrass approximation theorem and Bernstein's theorem (approximation theory).
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