was a Japanese
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who worked with
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s,
mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
and
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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
.
Kato studied physics and received his undergraduate degree in 1941 at the
Imperial University of Tokyo
, abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...
. After disruption of the
Second World War
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, 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
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...
in the United States.
Many works of Kato are related to mathematical physics. In 1951, he showed the self-adjointness of
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified 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.
"Tosio Kato (1917—1999)", Notices of the American Mathematical Society, June/July, 2000
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 AMS or Ams may refer to:
Organizations Companies
* Alenia Marconi Systems
* American Management Systems
* AMS (Advanced Music Systems)
* ams AG, semiconductor manufacturer
* AMS Pictures
* Auxiliary Medical Services
Educational institutions
* A ...
and SIAM
Thailand ( ), historically known as Siam () and officially the Kingdom of Thailand, is a country in Southeast Asia, located at the centre of the Mainland Southeast Asia, Indochinese Peninsula, spanning , with a population of almost 70 mi ...
. In 1970, he gave a plenary lecture at the ICM in Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...
(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.
See also
* Lie product formula
*Weyl–von Neumann theorem In mathematics, the Weyl–von Neumann theorem is a result in operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator () or Hilbert–Schmidt operator () of arbitrarily small norm, a bound ...
References
External links
*
{{DEFAULTSORT:Kato, Tosio
20th-century Japanese mathematicians
Mathematical physicists
People from Tochigi Prefecture
Academic staff of the University of Tokyo
University of California, Berkeley College of Letters and Science faculty
University of Tokyo alumni
1917 births
1999 deaths
PDE theorists
Operator theorists