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Paul G. Federbush
Regents' Proceedings 286

Paul G. Federbush, Ph.D., professor of mathematics in the College of Literature, Science, and the Arts, will retire from active faculty status on May 31, 2004.

Professor Federbush received his B.S. degree (1955) from the Massachusetts Institute of Technology and his M.A. (1958) and Ph.D. (1958) degrees from Princeton University. From 1958-66 he was on the faculty at M.I.T. Professor Federbush joined the University of Michigan faculty as a lecturer in 1966 and was promoted to associate professor in 1967 and professor in 1971.

A mathematical physicist, Professor Federbush studied the part of field theory that could be put on a firm mathematical foundation, and the applications of field theoretic ideas to other areas of mathematics. In 1969, he wrote an influential paper that was an infinitesimal version of Nelson's hypercontractive inequality in field theory. The Federbush inequality later became known as the logarithmic Sobolev inequality and is widely used in the theory of partial differential equations. Another paper, published in 1975, focused on the stability of matter and developed a new proof of a classic result of Dyson and Lenard that a large neutral system of electrons and nuclei does not collapse. His approach demonstrated that the technique of phase space localization is central to the proof. His most impressive result was the proof of "Debye" screening: in a charged, neutral gas the effects of the long-range electromagnetic interactions are screened out (1981). More recently, he developed a set of orthogonal phase space localized functions known as "wavelets," which are divergence free, and applied these wavelets to the Navier-Stokes equations of fluid dynamics.

Professor Federbush taught a wide range of courses in applied mathematics, mentored eleven doctoral students, and helped develop computer lab materials used today in the introductory differential equations course. He received a Sloan Foundation Fellowship in 1965 and a John Simon Guggenheim Memorial Fellowship in 1975, and he was a member of the Institute for Advanced Studies.

The Regents salute this distinguished scholar by naming Paul G. Federbush professor emeritus of mathematics.