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Tosio Kato, a longtime Professor of Mathematics at the University of California, Berkeley and a major researcher in nonlinear partial differential equations and in mathematical physics, passed away unexpectedly on October 2, 1999. He is survived by his wife Mizue, and his sister Ayako Ishiguro.
Professor Kato was a highly respected member of the international mathematics community.
He was born August 25, 1917, in Kanuma, Japan. He studied physics, earning the B.S. in 1941 and, after delays caused by World War II, the doctorate in 1951, both from the University of Tokyo. Professor Kato was appointed Assistant Professor of Physics at the University of Tokyo in 1951, and became Professor in 1958. He visited the United States several times during the 1950s, eventually decided to move here permanently, and became a member of the mathematics faculty at UC Berkeley in 1962.
Professor Kato published over 150 research papers during his long career. Among many honors, he won the Norbert Wiener Prize in Applied Mathematics in 1980, from the American Mathematics Society and the Society for Industrial and Applied Mathematics. Kato is also the author of a famous and influential monograph, Perturbation Theory for Linear Operators. He supervised three Ph.D. students from the University of Tokyo, and 21 from UC Berkeley.
In the spring of 1990, the Mathematical Sciences Research Institute at Berkeley sponsored a major mathematical conference in Kato's honor, attended by many of his former students, friends and colleagues. A tribute to his life and work, with many testimonials, may be found in the June/July 2000 issue of Notices of the American Mathematics Society.
Professor Kato was an intensely private person, with a deep interest in nature and especially the Botanical Gardens at Berkeley, which he often visited.
We believe that we can best honor Professor Kato's memory by outlining here some of his profound and lasting mathematical discoveries.
Mathematical quantum mechanics.
Kato achieved early mathematical fame with his proof, published in 1951, showing the self-adjointness of stationary Schrödinger operators for physically realistic singular potentials. This result crowned a program, initiated by John von Neumann, of providing a consistent mathematical foundation for nonrelativistic quantum mechanics. At about the same time Kato also established a rigorous quantum adiabatic theorem. He later revolutionized the field again in a paper from 1972 that introduced a novel analytic estimate now known as "Kato's inequality". His conjectures about square roots of accretive operators has profoundly influenced developments in Euclidean harmonic analysis. Kato also proved an important criterion for the absence of an embedded point spectrum.
Nonlinear evolution equations.
Throughout his life, Professor Kato was interested in the general theory of evolution equations, and he, in particular, laid the foundations for nonlinear evolution equations, most notably nonlinear symmetric hyperbolic equations. He pioneered work on what is sometimes called the "Kato bracket" in general Banach spaces.
Mathematical fluid mechanics.
Kato and Fujita introduced novel techniques into the study of weak solutions of the fundamental partial differential equations of incompressible fluid mechanics, the Navier-Stokes equations. In a famous paper with Beals and Majda he also discovered a diagnostic condition on the (possible) concentration of vorticity, the absence of which implies the existence of a strong solution.
Dispersive equations.
The Korteweg-de Vries (K-dV) equation is an important partial differential equation introduced originally to describe the propagation of shallow water waves. In 1983, Kato discovered the completely unexpected "Kato smoothing" effect, which has played a central role in the last decade's developments concerning the well-posedness of this equation and related nonlinear Schrödinger equations. The later Kato-Ponce commutator inequality originates with this work as well.
This incomplete recounting of Professor Kato's legacy to mathematics should make clear the extent of our loss.
Michael Christ
Lawrence C. Evans
Daniel Tataru
Maciej Zworski
Professor Kato was a highly respected member of the international mathematics community.
He was born August 25, 1917, in Kanuma, Japan. He studied physics, earning the B.S. in 1941 and, after delays caused by World War II, the doctorate in 1951, both from the University of Tokyo. Professor Kato was appointed Assistant Professor of Physics at the University of Tokyo in 1951, and became Professor in 1958. He visited the United States several times during the 1950s, eventually decided to move here permanently, and became a member of the mathematics faculty at UC Berkeley in 1962.
Professor Kato published over 150 research papers during his long career. Among many honors, he won the Norbert Wiener Prize in Applied Mathematics in 1980, from the American Mathematics Society and the Society for Industrial and Applied Mathematics. Kato is also the author of a famous and influential monograph, Perturbation Theory for Linear Operators. He supervised three Ph.D. students from the University of Tokyo, and 21 from UC Berkeley.
In the spring of 1990, the Mathematical Sciences Research Institute at Berkeley sponsored a major mathematical conference in Kato's honor, attended by many of his former students, friends and colleagues. A tribute to his life and work, with many testimonials, may be found in the June/July 2000 issue of Notices of the American Mathematics Society.
Professor Kato was an intensely private person, with a deep interest in nature and especially the Botanical Gardens at Berkeley, which he often visited.
We believe that we can best honor Professor Kato's memory by outlining here some of his profound and lasting mathematical discoveries.
Mathematical quantum mechanics.
Kato achieved early mathematical fame with his proof, published in 1951, showing the self-adjointness of stationary Schrödinger operators for physically realistic singular potentials. This result crowned a program, initiated by John von Neumann, of providing a consistent mathematical foundation for nonrelativistic quantum mechanics. At about the same time Kato also established a rigorous quantum adiabatic theorem. He later revolutionized the field again in a paper from 1972 that introduced a novel analytic estimate now known as "Kato's inequality". His conjectures about square roots of accretive operators has profoundly influenced developments in Euclidean harmonic analysis. Kato also proved an important criterion for the absence of an embedded point spectrum.
Nonlinear evolution equations.
Throughout his life, Professor Kato was interested in the general theory of evolution equations, and he, in particular, laid the foundations for nonlinear evolution equations, most notably nonlinear symmetric hyperbolic equations. He pioneered work on what is sometimes called the "Kato bracket" in general Banach spaces.
Mathematical fluid mechanics.
Kato and Fujita introduced novel techniques into the study of weak solutions of the fundamental partial differential equations of incompressible fluid mechanics, the Navier-Stokes equations. In a famous paper with Beals and Majda he also discovered a diagnostic condition on the (possible) concentration of vorticity, the absence of which implies the existence of a strong solution.
Dispersive equations.
The Korteweg-de Vries (K-dV) equation is an important partial differential equation introduced originally to describe the propagation of shallow water waves. In 1983, Kato discovered the completely unexpected "Kato smoothing" effect, which has played a central role in the last decade's developments concerning the well-posedness of this equation and related nonlinear Schrödinger equations. The later Kato-Ponce commutator inequality originates with this work as well.
This incomplete recounting of Professor Kato's legacy to mathematics should make clear the extent of our loss.
Michael Christ
Lawrence C. Evans
Daniel Tataru
Maciej Zworski
This University of California obituary is available at THIS LINK