Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to functional analysis, scattering theory, and servomechanisms.
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.
Phillips received the 1997 Leroy P. Steele Prize for Lifetime Achievement.
This work led to his book Theory of Servomechanisms,[4] which for many years was the standard text in the subject.
Philips's work (with A. Lubotzky and P. Sarnak) on Ramanujan graphs had a huge impact on combinatorics and computer science.