Sergei Natanovich 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.[1][2]
Work
Partial differential equations
In his doctoral dissertation, submitted in 1904 to the Sorbonne, Bernstein solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations.[3] 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.
Probability theory
In 1917, Bernstein suggested the first axiomatic foundation of probability theory, based on the underlying algebraic structure.[4] It was later superseded by the measure-theoretic approach of Kolmogorov.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.
Approximation theory
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.[5] In particular, he proved the Weierstrass approximation theorem[6][7] and Bernstein's theorem (approximation theory).
Publications
- 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
See also
- 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
Notes
- ↑ 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: 163. 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.
- ↑ 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: 17. 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
References
- O'Connor, John J.; Robertson, Edmund F., "Sergei Natanovich Bernstein", MacTutor History of Mathematics archive, University of St Andrews.
External links
- Sergei Natanovich Bernstein at the Mathematics Genealogy Project
- Sergei Natanovich Bernstein and history of approximation theory from Technion — Israel Institute of Technology
- Author profile in the database zbMATH