Sergei Bernstein: Difference between revisions
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===Approximation theory=== |
===Approximation theory=== |
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Through his application of [[Bernstein polynomial]]s, he laid the foundations of [[constructive function theory]], a field studying the connection between smoothness properties of a function and its approximations by polynomials.<ref>{{cite journal|first=V. S.|last=Videnskii|year=1961|journal=Russ. Math. Surv.|volume=16|page=17|title=Sergei Natanovich Bernshtein — founder of the constructive theory of functions|issue=2|doi=10.1070/RM1961v016n02ABEH004102|bibcode=1961RuMaS..16...17V}}</ref> In particular, he proved the [[Stone–Weierstrass theorem|Weierstrass approximation theorem]]<ref>S. Bernstein (1912–13) "Démonstration du théroème de Weierstrass, fondeé sur le calcul des probabilités, ''Commun. Soc. Math. Kharkow'' (2) 13: 1-2</ref><ref>Kenneth M. Lavasseur (1984) [https://www.jstor.org/stable/2322960 A Probabilistic Proof of the Weierstrass Theorem], [[American Mathematical Monthly]] 91(4): 249,50</ref> and [[Bernstein's theorem (approximation theory)]]. |
Through his application of [[Bernstein polynomial]]s, he laid the foundations of [[constructive function theory]], a field studying the connection between smoothness properties of a function and its approximations by polynomials.<ref>{{cite journal|first=V. S.|last=Videnskii|year=1961|journal=Russ. Math. Surv.|volume=16|page=17|title=Sergei Natanovich Bernshtein — founder of the constructive theory of functions|issue=2|doi=10.1070/RM1961v016n02ABEH004102|bibcode=1961RuMaS..16...17V}}</ref> In particular, he proved the [[Stone–Weierstrass theorem|Weierstrass approximation theorem]]<ref>S. Bernstein (1912–13) "Démonstration du théroème de Weierstrass, fondeé sur le calcul des probabilités, ''Commun. Soc. Math. Kharkow'' (2) 13: 1-2</ref><ref>Kenneth M. Lavasseur (1984) [https://www.jstor.org/stable/2322960 A Probabilistic Proof of the Weierstrass Theorem], [[American Mathematical Monthly]] 91(4): 249,50</ref> and [[Bernstein's theorem (approximation theory)]]. |
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==International Congress of Mathematicians== |
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Bernstein was an invited speaker at the [[International Congress of Mathematicians]] (ICM) in Cambridge, England in 1928 and in Bologna in 1928 and a plenary speaker at the ICM in Zurich.<ref>{{cite web|title=Bernstein, S.|website=ICM Plenary and Invited Speakers, International Mathematical Union|url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=bernstein}}</ref> His plenary address ''Sur les liaisons entre quantités aléatoires'' was read by [[Bohuslav Hostinsky]].<ref>{{cite web|title=1932 ICM - Zurich|website=MacTutor|url=https://mathshistory.st-andrews.ac.uk/ICM/ICM_Zurich_1932/}}</ref> |
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==Publications== |
==Publications== |
Revision as of 22:48, 2 September 2021
Sergei Bernstein | |
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Born | Sergei Natanovich Bernstein 5 March 1880 |
Died | 26 October 1968 | (aged 88)
Nationality | Soviet |
Alma mater | University of Paris |
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 |
Scientific career | |
Fields | Mathematics |
Institutions | University of Paris University of Göttingen University of Kharkiv Leningrad University Steklov Institute of Mathematics |
Doctoral advisor | Charles Émile Picard David Hilbert |
Doctoral students | Yakov Geronimus Sergey Stechkin |
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.[1][2]
Work
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.[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).
International Congress of Mathematicians
Bernstein was an invited speaker at the International Congress of Mathematicians (ICM) in Cambridge, England in 1928 and in Bologna in 1928 and a plenary speaker at the ICM in Zurich.[8] His plenary address Sur les liaisons entre quantités aléatoires was read by Bohuslav Hostinsky.[9]
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 (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
- ^ "Bernstein, S." ICM Plenary and Invited Speakers, International Mathematical Union.
- ^ "1932 ICM - Zurich". MacTutor.
References
- O'Connor, John J.; Robertson, Edmund F., "Sergei Bernstein", MacTutor History of Mathematics Archive, University of St Andrews
External links
- Sergei 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
- 1880 births
- 1968 deaths
- 19th-century Russian mathematicians
- 20th-century Russian mathematicians
- People from Kherson Governorate
- Corresponding Members of the Russian Academy of Sciences (1917–1925)
- Full Members of the USSR Academy of Sciences
- Moscow State University faculty
- National University of Kharkiv faculty
- University of Paris alumni
- Stalin Prize winners
- Recipients of the Order of Lenin
- Recipients of the Order of the Red Banner of Labour
- Approximation theorists
- Mathematical analysts
- Odessa Jews
- PDE theorists
- Probability theorists
- Scientists from Odessa
- Soviet mathematicians
- Burials at Novodevichy Cemetery
- Expatriates of the Russian Empire in France