Ralph S. Phillips
Encyclopedia
Ralph Saul Phillips was an American
mathematician and academic known for his contribution to functional analysis
, scattering theory
, and servomechanism
s. He served as a Professor of mathematics at Stanford University
. He made major contributions to acoustical scattering theory in collaboration with Peter Lax
, proving remarkable results on local energy decay and the connections between poles of the scattering matrix 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 for Lifetime Achievement.
at Los Angeles
(UCLA) in 1935 and his Ph.D. from the University of Michigan
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
, an instructor at the University of Washington
, and an instructor at Harvard University
. 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 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
. He moved to the University of Southern California
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.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician and academic known for his contribution to functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, scattering theory
Scattering theory
In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a...
, and servomechanism
Servomechanism
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...
s. He served as a Professor of mathematics at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
. He made major contributions to acoustical scattering theory in collaboration with Peter Lax
Peter Lax
Peter David Lax is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields...
, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on scattering theory
Scattering theory
In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a...
titled Scattering Theory for Automorphic Functions. Phillips received the 1997 Leroy P. Steele Prize 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 CaliforniaUniversity of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
at Los Angeles
Los Ángeles
Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...
(UCLA) in 1935 and his Ph.D. from the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
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, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, an instructor at the University of Washington
University of Washington
University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...
, and an instructor at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
. 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
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
, 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
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
. He moved to the University of Southern California
University of Southern California
The University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...
the next year and returned to UCLA in 1958. In 1960 he joined Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
and remained there until his death in 1998. He was the Robert Grimmett Professor of Mathematics at Stanford.
Books
- Scattering Theory for Automorphic Functions, with P. D. LaxPeter LaxPeter David Lax is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields...
. Princeton University PressPrinceton University Press-Further reading:* "". Artforum International, 2005.-External links:* * * * *...
(1977). ISBN 0691081840