Bernard Koopman

Bernard Osgood Koopman (born January 19, 1900 in Paris , France , † August 18, 1981 in Randolph , New Hampshire ) was an American mathematician.

Life

Koopman grew up in France and Italy, went to the USA with his family in 1915 and studied with George David Birkhoff at Harvard , where he received his bachelor's degree in 1922 and at Columbia University in 1926 with a thesis on dynamic systems (the classic celestial three-body problem ) (“On Rejection to Infinity and Exterior Motion in the Restricted Problem of Three Bodies”). Under Birkhoff's influence, he dealt with ergodic theory , which also gave rise to an occupation with the fundamentals of probability theory . From 1943 he was engaged in operations research when he was invited by Philip Morse to join the Operations Research Group (ORG) of the US Navy. In 1957/58 he was president of the Operations Research Society of America (OSRA), of which he was a founding member in 1952. He spent his entire career (apart from post-doc positions as Benjamin Pierce Instructor at Harvard and a year at Princeton University ) at Columbia University, where he became professor after World War II and Adrian professor in 1955. From 1951 to 1956 he was dean of the faculty. In addition, he continued to work in the field of operations research as a consultant at the Center of Naval Analyzes, the Institute for Defense Analyzes (IDA) (where he was 1956/7 and 1964/5) and the management consultancy Arthur D. Little Inc. 1959 to In 1961 he coordinated the US-UK military operations research application and NATO in London.

In his work on ergodic theory, which is important for the foundation of statistical mechanics (the ergodic hypothesis makes statements about the uniform distribution of orbits in the phase space of the dynamic system), he introduced methods of functional analysis . Observables are functions in phase space and the flow in phase space effects the mapping of observables in function space (a Hilbert space ) by linear time evolution operators, the spectrum of which is studied. In addition to Koopman's teacher Birkhoff, John von Neumann , who had previously developed the Hilbert space approach to quantum mechanics, demonstrated ergodic theorems in the early 1930s.

Francis Murray (1936), who researched operator algebras with John von Neumann, is one of his doctoral students .

In 1980 he received the ORSA Kimball Medal. In 1979 he received the Wander Award from the Military Operations Research Society.

literature

• Who's Who in America: a biographical dictionary of notable living men and women. : volume 33 (1964-1965), Marquis Who's Who, Chicago, Ill., 1964, p. 1125.
• Philip Morse , Obituary in Operations Research, Vol. 30, 1982, p. 417
• Koopman "Search and Screening", 1946, Persimmon Press 1980
• Birkhoff, Koopman: Recent contributions to ergodic theory, Proc. National Academy of Sciences, Vol. 18, 1932, p. 279

Web links

• Biography at OSRA