Sergei Natanovich Bernstein
| Sergei Natanovich Bernstein | |
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 Sergei Natanovich Bernstein
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| Born | 5 March 1880 Odessa, Imperial Russia |
| Died | 26 October 1968 (aged 88) Moscow, USSR |
| Residence | USSR |
| Fields | Mathematics |
| Institutions | University of Paris |
| 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; March 5, 1880, Odessa – October 26, 1968, Moscow) was a Russian and Soviet mathematician known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory.[1][2]
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[edit] Work
[edit] 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.
[edit] 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the first axiomatic foundation of probability theory, based on the underlying algebraic structure.[4] It was later superseded by the measure-theoretic approach of Kolmogorov.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 1920-s, he introduced a method for proving limit theorems for sums of dependent random variables.
[edit] Approximation theory
Bernstein 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 Bernstein's theorem (approximation theory).
[edit] Other fields
[edit] 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
[edit] 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
[edit] Notes
- ^ Youschkevitch, A. P.. "BERNSTEIN, SERGEY NATANOVICH". Dictionary of Scientific Biography. http://www.encyclopedia.com/doc/1G2-2830904824.html.
- ^ 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. http://iopscience.iop.org/0036-0279/16/2/A01.
- ^ Linnik, Ju. V. (1961). "The contribution of S. N. Bernšteĭn to the theory of probability". Russ. Math. Surv. 16 (2): 21–22. MR0130818.
- ^ Videnskii, V. S. (1961). "Sergei Natanovich Bernshtein — founder of the constructive theory of functions". Russ. Math. Surv. 16: 17. doi:10.1070/RM1961v016n02ABEH004102.
[edit] References
- O'Connor, John J.; Robertson, Edmund F., "Sergei Natanovich Bernstein", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Bernstein_Sergi.html.
