11/25/98

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David F. Salisbury, News Service (650) 725-1944;

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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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