Bernard Koopman

Bernard Osgood Koopman (* 1900, † 1981) was a born in France American mathematician.

Life and work

Koopman grew up in France and Italy, went with his family in 1915 in the United States and studied with George David Birkhoff at Harvard, where he 1922 a bachelor's degree made ​​and 1926 at Columbia University with a thesis on dynamic systems (the classic sky mechanical three-body problem received his doctorate ) ("On Rejection to Infinity and Exterior Motion in the Restricted problem of Three Bodies" ). Under Birkhoff's influence, he worked on ergodic theory, which also results in a study of the basics of probability theory arose. From 1943 he worked on Operations Research, when he was invited by Philip Morse to join the Operations Research Group ( ORG) of the U.S. Navy. He was in 1957/58 President of the Operations Research Society of America ( OSRA ), he was one of the founding members in 1952. He spent his entire career ( up to post - doc positions as Benjamin Pierce Instructor at Harvard and a year at Princeton University) at Columbia University, where he was after the Second World War, Professor and in 1955 Professor Adrian. From 1951 to 1956 he was dean of the faculty. In addition, he continued working in the field of Operations Research research as a consultant at the Center of Naval Analyses, the Institute for Defense Analyses ( IDA) ( where 1956/7 and 1964/5 he was) and the consulting firm Arthur D. Little, Inc. 1959 to in 1961 he coordinated the military operations research application between the U.S. and the UK and NATO in London.

In his work on ergodic theory, which is important for the foundations of statistical mechanics ( the ergodic hypothesis makes statements about the equal distribution of trajectories in the phase space of the dynamical system ), he introduced methods of functional analysis. Observables are functions on the phase space and the flow in the phase space causes the image of the observables in function space ( a Hilbert space ) by linear time evolution operators whose spectrum is studied. Picking up Koopman 's approach proved next Koopmans teacher Birkhoff and John von Neumann, who had previously developed the Hilbert space approach to quantum mechanics, Ergodentheoreme the early 1930s.

One of his graduate students Francis Murray ( 1936), who studied with John von Neumann operator algebras.

In 1980 he received the Kimball Medal of ORSA. In 1979 he received the Award of hiking Military Operations Research Society.