Ralph Phillips

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Ralph Saul Phillips (born June 23, 1913 in Oakland , California - † November 23, 1998 ) was an American mathematician who a. a. dealt with analysis .

Live and act

Phillips studied at the University of California, Los Angeles (Bachelor 1935) and received his doctorate in 1939 at the University of Michigan under Theophil Henry Hildebrandt . From 1938 to 1940 (and 1950/1) he was at the Institute for Advanced Study . He then was an instructor at the University of Washington and Harvard University . During the Second World War he led a group at the Radiation Laboratory of the Massachusetts Institute of Technology (MIT), which was particularly dedicated to radar development. He was then an assistant professor at the Courant Institute of Mathematical Sciences of New York University , at the University of Southern California and in 1958 at the University of California, Los Angeles. In 1960 he went to Stanford University , where he was a professor until his retirement.

Phillips dealt with semigroups of linear operators in functional analysis (about which he wrote an authoritative book with Einar Hille ). With Peter Lax he developed geometric time-dependent methods for solving the wave equation in areas outside of compact "obstacles", that is, the scattering theory , whereby they also examined the connection to the poles of the S matrix . With Lax and Peter Sarnak he worked on the theory of automorphic forms , especially in connection with scattering theory on symmetric spaces . In a 1976 published book by Lax he examined the possibility the spectrum of the Laplace operator on such spaces and proved the Selberg - trace formula . In 1988 he introduced Ramanujan graphs with Peter Sarnak and Alexander Lubotzky .

In 1954/55 and 1974 he was a Guggenheim Fellow. In 1997 he received the Leroy P. Steele Prize for his life's work . In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Scattering theory for hyperbolic systems ) and in 1966 in Moscow ( Scattering Theory with Peter Lax). In 1971 he was elected to the American Academy of Arts and Sciences . Phillips was a passionate sailor, his sailboat was called "Wave equation".

His doctoral students include Andrew Majda and Michael Reed .

Fonts

  • with H. James, N. Nichols (editors) The Theory of Servomechanisms (MIT Radiation Lab), McGraw Hill 1947
  • with Einar Hille: Functional Analysis and Semigroups , AMS 1957
  • with Peter Lax: Scattering Theory , Academic Press 1967, 2nd edition 1989 (with attachments by Cathleen Synge Morawetz and G. Schmidt)
  • with Peter Lax: Scattering theory for automorphic functions , Princeton University Press 1976
  • Reminiscences about the 1930s , Mathematical Intelligencer, Vol. 16, 1994, p. 6

Web links

Individual evidence

  1. ↑ Alexander Lubotzky, Ralph Phillips, Peter Sarnak: Ramanujan graphs. Combinatorica, Vol. 8, 1988, pp. 261-277
personal data
SURNAME Phillips, Ralph
ALTERNATIVE NAMES Phillips, Ralph Saul (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 23, 1913
PLACE OF BIRTH Oakland , California
DATE OF DEATH November 23, 1998