Tosio Kato

Tosio Kato (Japanese加藤 敏夫, Katō Toshio, born August 25, 1917 in Kanuma, † October 2, 1999 in Oakland, California ) was a Japanese mathematician who worked on partial differential equations, mathematical physics and functional analysis.

Life

Kato studied physics and did his undergraduate degree in 1941 at the University of Tokyo. After an interruption by the Second World War, he received his doctorate in 1951 at the University of Tokyo, where he became professor in 1958. From 1962 he worked as a professor at the University of Berkeley in the U.S..

Many works of Kato related to mathematical physics. In 1951, he showed the self-adjointness of Hamiltonians of quantum mechanics for realistic ( singular ) potentials. He dealt with nonlinear evolution equations, the Korteweg - de Vries equation ( Kato smoothing effect 1983) and with solutions of the Navier -Stokes equation. In the Navier -Stokes equation in three dimensions one of the open problems is the question of the existence of regular, clear solutions (dissolved in two dimensions by Jean Leray ), one of the Millennium Problems. Kato has taken a new approach to semi- groups and scaling arguments due to the fractal nature of the solutions and proved the global existence of unique regular solutions in three dimensions, if the initial data is not " too large" are. Kato is also known for his influential book, Perturbation theory of linear operators, published by Springer -Verlag.

In 1960 he was awarded the Asahi Prize. In 1980 he won the Norbert Wiener Prize in Applied Mathematics from SIAM. In 1970 he gave a plenary lecture at the ICM in Nice ( Scattering theory and perturbation of continuous spectra ).

Writings

  • Perturbation theory of linear operators. Basic teachings of the mathematical sciences, Springer-Verlag 1966, 1976.
  • A short introduction to the perturbation theory of linear operators. Springer -Verlag 1982.
  • Quasi- linear equations of evolution, with applications to partial differential equations, in: Spectral theory and differential equations ( Proc. Sympos, Dundee, 1974; dedicated to Konrad Jörgensmann. ), Springer, Berlin, 1975, Lecture Notes in Math, Vol. 448, pp. 25-70
Kanuma, Tochigi Self-adjoint operator Society for Industrial and Applied Mathematics Integrated Authority File
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