Education
Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. Kakutani received his Doctor of Philosophy in 1941 from Osaka University and taught there through World World War World War II
角谷 静夫
mathematician university professor
Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. Kakutani received his Doctor of Philosophy in 1941 from Osaka University and taught there through World World War World War II
At one point he spent two years at the Institute for Advanced Study in Princeton at the invitation of the mathematician Hermann Weyl. While there, he also met John von Neumann. The Kakutani fixed-point theorem is a generalization of Brouwer"s fixed-point theorem, holding for generalized correspondences instead of functions.
Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory.
Kakutani"s other mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems). They also include his solution of the Poisson equation using the methods of stochastic analysis.
The Collatz conjecture is also known as the Kakutani conjecture.
He returned to the Institute for Advanced Study in 1948, and was given a professorship by Yale in 1949, where he won a students choice award for excellence in teaching. Kakutani received two 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.
