Education
University of Michigan. University of California, Los Los Angeles
( The application by Fadeev and Pavlov of the Lax-Phillip...)
The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula. CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula.
http://www.amazon.com/gp/product/0691081840/?tag=2022091-20
(This revised edition of a classic book, which established...)
This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.
http://www.amazon.com/gp/product/0124400515/?tag=2022091-20
University of Michigan. University of California, Los Los Angeles
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 was born in Oakland on 23 June 1913.
He received his bachelor’s degree from the University of California at Los Angeles (University of California, Los Angeles) in 1935 and his Doctor of Philosophy from the University of Michigan in 1939 under the direction of Theophil H. Hildebrandt. 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 University of California, Los Angeles 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 had a huge impact on combinatorics and computer science.
( The application by Fadeev and Pavlov of the Lax-Phillip...)
( The application by Fadeev and Pavlov of the Lax-Phillip...)
(This revised edition of a classic book, which established...)
(The Colloquium series bestseller.)
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.