Sergei Natanovich Bernstein
Sergei Natanovich Bernstein | |
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Sergei Natanovich Bernstein
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Born | Odessa, Kherson Governorate, Russian Empire |
5 March 1880
Died | Script error: The function "death_date_and_age" does not exist. 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]
Contents
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the first axiomatic foundation of probability theory, based on the underlying algebraic structure.[4] It was later superseded by the measure-theoretic approach of Kolmogorov.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
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).
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
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References
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External links
- Pages with broken file links
- Articles containing Russian-language text
- 1880 births
- 1968 deaths
- People from Odessa
- People from Kherson Governorate
- Ukrainian Jews
- Approximation theorists
- Probability theorists
- 19th-century mathematicians
- 20th-century mathematicians
- Soviet mathematicians
- Mathematical analysts
- Ukrainian mathematicians
- PDE theorists
- University of Paris alumni
- University of Kharkiv faculty