Tosio Kato
Encyclopedia
was a Japanese mathematician
who worked with partial differential equation
s, 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 Hamiltonian
s 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. 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).
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who worked with partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
and functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
.
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
University of Tokyo
, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
, 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 Hamiltonian
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
s 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. 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
Norbert Wiener Prize in Applied Mathematics
The Norbert Wiener Prize in Applied Mathematics is a $5000 prize awarded every three years to for an outstanding contribution to "applied mathematics in the highest and broadest sense." It was endowed in 1967 in honor of Norbert Wiener by MIT's mathematics department and is provided jointly by the...
from AMS
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
and SIAM
Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
. In 1970, he gave a plenary lecture at the ICM
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Nice
Nice
Nice is the fifth most populous city in France, after Paris, Marseille, Lyon and Toulouse, with a population of 348,721 within its administrative limits on a land area of . The urban area of Nice extends beyond the administrative city limits with a population of more than 955,000 on an area of...
(scattering theory and perturbation of continuous spectra).
Publications
- 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.