Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to

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, norm, topology, etc.) and the linear functions defined o ...

, scattering theory, and servomechanisms. He served as a Professor of mathematics at Stanford University. He made major contributions to acoustical scattering theory in collaboration with

Peter Lax Peter David Lax (born Lax Péter Dávid; 1 May 1926) is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics. Lax has made important contributions to integrable systems, fluid ...

, proving remarkable results on local energy decay and the connections between poles of the

scattering matrix In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More forma ...

and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on scattering theory titled ''Scattering Theory for Automorphic Functions''. Phillips received the 1997

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Lifetime Achievement.

Education and career

Phillips was born in Oakland on 23 June 1913. He received his bachelor's degree from the

University of California The University of California (UC) is a public land-grant research university system in the U.S. state of California. The system is composed of the campuses at Berkeley, Davis, Irvine, Los Angeles, Merced, Riverside, San Diego, San Franci ...

Los Angeles Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the List of municipalities in California, largest city in the U.S. state, state of California and the List of United States cities by population, sec ...

(UCLA) in 1935 and his Ph.D. from the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

in 1939 under the direction of Theophil H. Hildebrandt. From 1939 until 1942 he was a member of the Institute for Advanced Study in

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

, an instructor at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattl ...

, and an instructor at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

. It was at the University of Washington he met his future wife, Jean. During the war he led a research group at the Radiation Laboratory at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

, the facility where much of the theoretical and practical work on radar technology was done. This work led to his book Theory of Servomechanisms, which for many years was the standard text in the subject. After the war he returned to mathematics, joining as an assistant professor at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

. He moved to the

University of Southern California , mottoeng = "Let whoever earns the palm bear it" , religious_affiliation = Nonsectarian—historically Methodist , established = , accreditation = WSCUC , type = Private research university , academic_affiliations = , endowment = $8.1 ...

the next year and returned to UCLA in 1958. In 1960 he joined Stanford University and remained there until his death in 1998. He was the Robert Grimmett Professor of Mathematics at Stanford. Philips's work (with A. Lubotzky and P. Sarnak) on

Ramanujan graphs In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders. AMurty's survey papernotes, Ram ...

had a huge impact on combinatorics and

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...

Books

*''Scattering Theory for Automorphic Functions'', with P. D. Lax.

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financia ...

(1977).

References

External links

*
Ralph S. Phillips, editorial in ''Journal of Evolution Equations''
{{DEFAULTSORT:Phillips, Ralph S. 1913 births 1998 deaths 20th-century American mathematicians University of California, Los Angeles alumni University of Michigan alumni University of California, Los Angeles faculty Stanford University Department of Mathematics faculty Courant Institute of Mathematical Sciences faculty