# Hitoshi Kumano-Go

### Born: 4 October 1935 in Arita, Wakayama Prefecture, Japan

Died: 24 August 1982 in Osaka, Japan

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**Hitoshi Kumano-Go**was educated in the standard way for gifted students in Japan at this time. Before entering university he studied at Taikyu Senior High School, graduating in 1958.

Entering Osaka University after graduating from high school, Kumano-Go studied mathematics and graduated in 1958. He continued to study at Osaka University for his doctorate. His supervisor was M Nagumo who supervised his work on the singular perturbation of second order partial differential equations. As is frequently the case, the problem which Kumano-Go studied was to extend work which had been completed earlier by his supervisor.

In 1962 Kumano-Go was appointed as an assistant at Osaka University. He submitted his doctoral dissertation in 1963 and received his Ph.D. in September of that year. He continued on the staff at Osaka, being promoted to assistant professor in 1964 and to associate professor in 1967.

During these years Kumano-Go published a series of papers which studied the local and global uniqueness of the solutions of the Cauchy problem for partial differential equations. This work used ideas from earlier contributions to the topic by Calderon and Zygmund. In two papers Kumano-Go also studied non-uniqueness of solutions of the Cauchy problem.

Kumano-Go spent the two academic years 1967-69 visiting the Courant Institute of Mathematical Sciences at New York University. These were years of great benefit to Kumano-Go who was able to develop many ideas in conversations with Kurt Friedrichs, Peter Lax, Louis Nirenberg and others. He became involved in founding the theory of pseudo-differential operators and after his return to Osaka he continued to publish important contributions to this topic.

In 1971 Kumano-Go was promoted to full professor. His major treatise on

*Pseudo Differential Operators*was published in Japanese in 1974. It is [2]:-

The book has been translated into English and appeared, published by MIT Press, in 1982.... an outstanding contribution to the field of pseudo-differential operators in view of its uniqueness and the wealth of material.

One other important monograph written by Kumano-Go should be mentioned. This is

*Partial differential equations*which was again written in Japanese and was published in 1978. This is a textbook which in addition to studying partial differential equations provides an introduction to pseudo-differential operators.

In addition to his work on pseudo-differential operators, Kumano-Go published a series of papers on the product of Fourier integral operators. This collaborative work with his colleagues led to results which were applied to [2]:-

H Tanabe writes in [2] about Kumano-Go mathematical contributions other than those contained in his research:-... the construction of the fundamental solution of a first order hyperbolic system and the study of the wave front sets of solutions.

Kumano-Go suffered ill health and was admitted to Osaka Hospital in May 1981. The doctors discovered that he was suffering from a brain tumour from which no cure was possible. At the height of his mathematical contributions at the age of 46, Kumano-Go sadly died.Kumano-Go's contributions were not limited to his own personal mathematical achievements. He also trained many young mathematicians of high ability. He was well known for the kindly interest which he took in the careers of young mathematicians. He was always ready to help, encourage and advise them. He looked through all their manuscripts, helping to improve and develop their ideas.

**Article by:** *J J O'Connor* and *E F Robertson*

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