Shizuo Kakutani

Shizuo Kakutani

nihongo|Shizuo Kakutani|角谷 静夫|Kakutani Shizuo|August 28, 1911–August 17, 2004 was a Japanese mathematician, best known for his eponymous fixed-point theorem.

Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. Early in his career he spent two years at the Institute for Advanced Study in Princeton at the invitation of the German mathematician Hermann Weyl. While there, he also met John von Neumann.

Kakutani received his Ph.D. in 1941 from Osaka University [MathGenealogy|id=1401] and taught there through World War II. He returned to the Institute for Advanced Study in 1948, and was given a professorship by Yale in 1949.

Kakutani received two major awards of the Japan Academy, the Imperial Prize and the Academy Prize in 1982, for his scholarly achievements in general and his work on functional analysis in particular.

The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important use is in proving the existence of Nash equilibria in game theory.

Kakutani's other well-known mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory, and his solution of the Poisson equation using the methods of stochastic analysis.

The Collatz conjecture is also known as the Kakutani conjecture.

His daughter, Michiko Kakutani, is a Pulitzer Prize-winning literary critic for the "New York Times".

See Also

Kakutani fixed point theorem

List of books available in English

*"Selected papers" / Shizuo Kakutani ; Robert R. Kallman, editor (1986)

References

External links

* [http://www.nytimes.com/2004/08/18/obituaries/18kakutani.html New York Times obituary]
* [http://www.uml.edu/Dept/Math/alumni/tangents/tangents_Fall2004/MathInTheNews.htm Obituary, University of Massachusetts newsletter]
* [http://www.yale.edu/opa/v33.n1/story10.html Obituary, Yale Bulletin and Calendar]
* [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kakutani.html Biography, University of St. Andrews/Turnbull]
* [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kakutani.html The Lost Theorems of Kakutani]


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  • Shizuo Kakutani — (1970). Shizuo Kakutani (角谷 静夫, Kakutani Shizuo? …   Wikipedia Español

  • Shizuo Kakutani — (1970) Shizuo Kakutani (jap. 角谷 静夫, Kakutani Shizuo; * 28. August 1911 in Ōsaka; † 17. August 2004 in New Haven, Connecticut) war ein japanisch amerikanischer Mathematiker. Kakutani besuchte die Universität Tohoku, dort war Tatsujiro Shimizu sein …   Deutsch Wikipedia

  • Kakutani — is a surname, and may refer to:* Michiko Kakutani (born 1955), Japanese American Pulitzer Prize winning critic * Shizuo Kakutani (1911 2004), Japanese mathematician known for the Kakutani fixed point theorem …   Wikipedia

  • Kakutani — ist der Name folgender Personen: Michiko Kakutani (* 1955), amerikanische Literaturkritikerin Shizuo Kakutani (1911–2004), japanisch amerikanischer Mathematiker. Diese Seite ist eine Begriffsklärung zur Unterscheidung mehr …   Deutsch Wikipedia

  • Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… …   Wikipedia

  • Teorema del punto fijo de Kakutani — En análisis matemático el teorema del punto fijo de Kakutani, (llamado así en honor a Shizuo Kakutani quien lo demostró en 1941), es una generalización del teorema del punto fijo de Brouwer que describe condiciones para las cuales una función… …   Wikipedia Español

  • Fixpunktsatz von Kakutani — Eine Korrespondenz von einer Menge A in eine Menge B ist eine Abbildung φ von A in die Potenzmenge von B. Damit handelt es sich um eine Präzisierung des in der älteren mathematischen Literatur häufiger anzutreffenden Begriffs der mehrwertigen… …   Deutsch Wikipedia

  • Michiko Kakutani — (角谷 美智子, Kakutani Michiko?, born January 9, 1955) is an American Pulitzer Prize winning critic for The New York Times and is considered by many to be a leading literary critic in the United States.[1][2] …   Wikipedia

  • Michiko Kakutani — (* 9. Januar 1955 in New Haven, Connecticut) ist eine amerikanische Literaturkritikerin. Als Hauptrezensentin der New York Times zählt sie zu den einflussreichsten, zugleich aber auch zu den umstrittensten Literaturkritikern der USA. Sie wurde… …   Deutsch Wikipedia

  • Stochastic processes and boundary value problems — In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani s 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion.… …   Wikipedia

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