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Sergei Bernstein

January 06, 2023

Sergei Natanovich Bernstein (Russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as Bernshtein; 5 March 1880 – 26 October 1968) was a Ukrainian 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the first axiomatic foundation of probability theory, based on the underlying algebraic structure.[4] It was later superseded by the measure-theoretic approach of Kolmogorov.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). Bernstein polynomials also form the mathematical basis for Bézier curves, which later became important in computer graphics.

International Congress of Mathematicians

Bernstein was an invited speaker at the International Congress of Mathematicians (ICM) in Cambridge, England in 1912 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

Notes

  1. ^ Youschkevitch, A. P. "BERNSTEIN, SERGEY NATANOVICH". Dictionary of Scientific Biography.
  2. ^ 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.
  3. ^ 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ S. Bernstein (1912–13) "Démonstration du théroème de Weierstrass, fondeé sur le calcul des probabilités, Commun. Soc. Math. Kharkow (2) 13: 1-2
  7. ^ Kenneth M. Lavasseur (1984) A Probabilistic Proof of the Weierstrass Theorem, American Mathematical Monthly 91(4): 249,50
  8. ^ "Bernstein, S." ICM Plenary and Invited Speakers, International Mathematical Union.
  9. ^ "1932 ICM - Zurich". MacTutor.

References

External links

January 06, 2023
sergei, bernstein, sergei, natanovich, bernstein, russian, Серге, Ната, нович, Бернште, йн, sometimes, romanized, bernshtein, march, 1880, october, 1968, ukrainian, russian, mathematician, jewish, origin, known, contributions, partial, differential, equations,. Sergei Natanovich Bernstein Russian Serge j Nata novich Bernshte jn sometimes Romanized as Bernshtein 5 March 1880 26 October 1968 was a Ukrainian and Russian mathematician of Jewish origin known for contributions to partial differential equations differential geometry probability theory and approximation theory 1 2 Sergei BernsteinBornSergei Natanovich Bernstein 1880 03 05 5 March 1880Odessa Kherson Governorate Russian EmpireDied26 October 1968 1968 10 26 aged 88 Moscow Soviet UnionNationalitySovietAlma materUniversity of ParisKnown forBernstein 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 geneticsScientific careerFieldsMathematicsInstitutionsUniversity of Paris University of Gottingen University of Kharkiv Leningrad UniversitySteklov Institute of MathematicsDoctoral advisorCharles Emile PicardDavid HilbertDoctoral studentsYakov GeronimusSergey Stechkin Contents 1 Work 1 1 Partial differential equations 1 2 Probability theory 1 3 Approximation theory 2 International Congress of Mathematicians 3 Publications 4 See also 5 Notes 6 References 7 External linksWork EditPartial differential equations Edit 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 Edit 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 Edit 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 Bernstein polynomials also form the mathematical basis for Bezier curves which later became important in computer graphics International Congress of Mathematicians EditBernstein was an invited speaker at the International Congress of Mathematicians ICM in Cambridge England in 1912 and in Bologna in 1928 and a plenary speaker at the ICM in Zurich 8 His plenary address Sur les liaisons entre quantites aleatoires was read by Bohuslav Hostinsky 9 Publications EditS 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 1946See also EditA 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 theoremNotes Edit 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 Bernsteĭn 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 Demonstration du theroeme de Weierstrass fondee sur le calcul des probabilites 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 EditO Connor John J Robertson Edmund F Sergei Bernstein MacTutor History of Mathematics archive University of St AndrewsExternal links EditSergei 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 Retrieved from https en wikipedia org w index php title Sergei Bernstein amp oldid 1113782323, wikipedia, wiki, book, books, library,

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