Sergei Natanovich Bernstein
5 March 1880
|Died||26 October 1968 (aged 88)|
|Alma mater||University of Paris|
|Known for||Bernstein's inequality in analysis |
Bernstein inequalities in probability theory
Bernstein's theorem (approximation theory)
Bernstein's theorem on monotone functions
Bernstein problem in mathematical genetics
|Institutions||University of Paris|
University of Göttingen
University of Kharkiv
Steklov Institute of Mathematics
|Doctoral advisor||Charles Émile Picard|
|Doctoral students||Yakov Geronimus|
Sergei Natanovich Bernstein (Russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as Bernshtein; 5 March 1880 – 26 October 1968) was a Soviet and Russian mathematician of Jewish origin known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory.
Partial differential equations
In his doctoral dissertation, submitted in 1904 to 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 It was later superseded by the measure-theoretic approach of Kolmogorov.
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).
- S. N. Bernstein, Collected Works (Russian):
- vol. 1, The Constructive Theory of Functions (1905–1930), translated: Atomic Energy Commission, Springfield, Va, 1958
- vol. 2, The Constructive Theory of Functions (1931–1953)
- vol. 3, Differential equations, calculus of variations and geometry (1903–1947)
- vol. 4, Theory of Probability. Mathematical statistics (1911–1946)
- S. N. Bernstein, The Theory of Probabilities (Russian), Moscow, Leningrad, 1946
- A priori estimate
- Bernstein algebra
- Bernstein's inequality (mathematical analysis)
- Bernstein inequalities in probability theory
- Bernstein polynomial
- Bernstein's problem
- Bernstein's theorem (approximation theory)
- Bernstein's theorem on monotone functions
- Bernstein–von Mises theorem
- Stone–Weierstrass theorem
- Youschkevitch, A. P. "BERNSTEIN, SERGEY NATANOVICH". Dictionary of Scientific Biography.
- Lozinskii, S. M. (1983). "On the hundredth anniversary of the birth of S. N. Bernstein". Russ. Math. Surv. 38 (3): 163. Bibcode:1983RuMaS..38..163L. doi:10.1070/RM1983v038n03ABEH003497.
- Akhiezer, N.I.; Petrovskii, I.G. (1961). "S. N. Bernshtein's contribution to the theory of partial differential equations". Russ. Math. Surv. 16 (2): 1–15. Bibcode:1961RuMaS..16....1A. doi:10.1070/RM1961v016n02ABEH004101.
- Linnik, Ju. V. (1961). "The contribution of S. N. Bernšteĭn to the theory of probability". Russ. Math. Surv. 16 (2): 21–22. doi:10.1070/rm1961v016n02abeh004103. MR 0130818.
- Videnskii, V. S. (1961). "Sergei Natanovich Bernshtein — founder of the constructive theory of functions". Russ. Math. Surv. 16 (2): 17. Bibcode:1961RuMaS..16...17V. doi:10.1070/RM1961v016n02ABEH004102.
- S. Bernstein (1912–13) "Démonstration du théroème de Weierstrass, fondeé sur le calcul des probabilités, Commun. Soc. Math. Kharkow (2) 13: 1-2
- Kenneth M. Lavasseur (1984) A Probabilistic Proof of the Weierstrass Theorem, American Mathematical Monthly 91(4): 249,50
- O'Connor, John J.; Robertson, Edmund F., "Sergei Bernstein", MacTutor History of Mathematics archive, University of St Andrews