Tosio Kato

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Tosio Kato
Tosio kato.JPG
Born (1917-08-25)August 25, 1917
Kanuma, Tochigi, Japan
Died October 2, 1999(1999-10-02) (aged 82)
Oakland, USA
Citizenship Japan
Fields Mathematics
Institutions University of Tokyo
University of California at Berkeley
Alma mater Imperial University of Tokyo
Doctoral advisor Kwan-ichi Terazawa
Doctoral students Preben Alsholm
Charles Amelin
Erik Balslev
Andrew Childs
Gilles Darmois
Charles Fisher
Hiroshi Fujita
James Howland
Teruo Ikebe
Rafael Iorio, Jr.
Shige Kuroda
Chi-Yuen Lai
Charles Lin
Frank Massey
Francis McGrath
Joel Mermin
Masaomi Nakata
Dung Nguyen
Gershon Pinchuk
Ronald Riddell
Hugh Stewart
Ponnaluri Suryanarayana
Howard Swann
Baoswan Wong-Dzung
Known for Kato's conjecture
Heinz–Kato inequality
Kato Rellich Theorem
Notable awards Asahi Prize (1960)
Norbert Wiener Prize in Applied Mathematics (1980)

Tosio Kato (加藤 敏夫, Katō Toshio, August 25, 1917 – October 2, 1999) was a Japanese mathematician who worked with partial differential equations, mathematical physics and functional analysis.

Kato studied physics and received his undergraduate degree in 1941 at the Imperial University of Tokyo. After disruption of the Second World War, he received his doctorate in 1951 from the University of Tokyo, where he became a professor in 1958. From 1962, he worked as a professor at the University of California at Berkeley in the United States.

Many works of Kato are related to mathematical physics. In 1951, he showed the self-adjointness of Hamiltonians for realistic (singular) potentials. He dealt with nonlinear evolution equations, the Korteweg–de Vries equation (Kato smoothing effect in 1983) and with solutions of the Navier-Stokes equation.[1][2] Kato is also known for his influential book Perturbation theory of linear operators, published by Springer-Verlag.

In 1980, he won the Norbert Wiener Prize in Applied Mathematics from AMS and SIAM. In 1970, he gave a plenary lecture at the ICM in Nice (scattering theory and perturbation of continuous spectra).


  • Perturbation theory of linear operators. Principles of Mathematical Sciences, Springer-Verlag, 1966, 1976.
  • A short introduction to the perturbation theory of linear operators. Springer-Verlag 1982.


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