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Prominent mathematician dies at 85

Ralph S. Phillips, a professor emeritus in the Mathematics Department at Stanford University, and nationally prominent member of the mathematical community, died Nov. 23, 1998, as a consequence of a lymphoma-related illness. Phillips was chairman of the Stanford Mathematics Department from 1970 to 1973, and in 1977 was appointed to the Robert Grimmett Chair of Mathematics.

Born on June 23, 1913 in Oakland, Calif., Phillips received his bachelor's degree at UCLA in 1935 and his Ph.D. from the University of Michigan in 1939. After earning his doctorate he was a member of the Institute for Advanced Study in Princeton in 1939-1940, where he worked alongside such well-known mathematicians as John von Neumann and Paul Erdös. Phillips was an instructor at the University of Washington in 1940-1941, where he met his future wife Jean, who was working as a teaching assistant. They moved together to Cambridge, Mass. where he held another instructorship at Harvard during 1941-1942.

A few years ago Phillips wrote an article (Mathematical Intelligencer, Vol.16 No. 3, 1994) about the prevalence of anti-Semitism in the academic culture of that period, and how it influenced his life at that time.

During the war he was the leader of a research group at MIT's Radiation Laboratory, the facility where much of the basic theoretical and practical work in radar technology was done and which later became Lincoln Laboratories. After the war, in 1946, he returned to mathematics and became an assistant professor at the Courant Institute of Mathematical Sciences at New York University. He moved to the University of Southern California the next year and moved again to UCLA in 1958; he was appointed Professor at Stanford in 1960.

Phillips was a Guggenheim Fellow in 1954 and again in 1974, and was elected to the American Academy of Arts and Sciences in 1971. He was a founding editor, with well-known mathematicians Paul Malliavin and Irving Segal, of the Journal of Functional Analysis in 1966.

Phillips is regarded as one of the leading analysts of his time. There were three main phases to his research career. In the first he worked in the theory of semigroups, a field in functional analysis which has relevance to the theory of linear and nonlinear heat conduction. The next phase of his career centered around a long collaboration with Peter Lax of the Courant Institute. Their work revolutionized the field of scattering theory for linear hyperbolic partial differential equations, a central topic in mathematical physics which includes acoustical and quantum mechanical scattering. The so-called ``Lax-Phillips'' theory was born as a result of these endeavors.

The final stage of his career, for the most part conducted after his retirement in 1978, was very active. It involved, among other themes, application of Lax-Phillips theory to the study of the spectral theory of the Laplace operator on symmetric spaces. Part of this work was joint with Peter Sarnak (now at Princeton) and other young researchers. He was a prominent counterexample to the common view that mathematicians do their best work in their youth. The quality and quantity of his research never flagged. In 1996 he was awarded the Steele Prize for Lifetime Achievement by the American Mathematical Society.

Phillips was for many years an enthusiastic sailor and had numerous friends all over the world. His wife Jean died in 1997. He is survived by his sister Leah Duchowny of Los Angeles, his daughter Xanthippe of Berkeley and one grandson.

The department will hold a commemorative event some time in January.



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