Sergei Bernstein

Sergei Natanovich Bernstein
Sergei Natanovich Bernstein
Born	(1880-03-05)5 March 1880 Odessa, Kherson Governorate, Russian Empire
Died	26 October 1968(1968-10-26) (aged 88) Moscow, Soviet Union
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 Goettingen University of Kharkiv Leningrad University Steklov Institute of Mathematics
Doctoral advisor	Charles Émile Picard David Hilbert
Doctoral students	Vladimir Brzhechka Yakov Geronimus Vasilii Goncharov Boris Rymarenko Sergey Stechkin

Sergei Natanovich Bernstein (Russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as [Bernshtein] Error: {{Lang}}: text has italic markup (help); 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.

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. 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. It was later superseded by the measure-theoretic approach of Kolmogorov.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. In particular, he proved the Weierstrass approximation theorem 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

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