George Mackey
George Whitelaw Mackey ( February 1, 1916 in St. Louis, † March 15 2006 in Belmont (Massachusetts ) ) was an American mathematician.
George Mackey grew up in Houston in Texas, where he began his studies of physics, chemical engineering and mathematics at Rice Institute. His studies in mathematics, he continued at Harvard University, where in Marshall Harvey Stone, he received his doctorate in 1942 with a thesis on locally convex topologies in vector spaces (introduction of the Mackey topology). After a stopover at the Illinois Institute of Technology, Caltech and the Institute for Advanced Study ( 1941) in Princeton, he returned as an instructor in 1943 returned to Harvard and remained there - from 1956 as a professor ( from 1969 to Landon T. Clay Professor for Mathematics ) -. until his retirement in 1985 his main areas of work were representation theory, ergodic theory, functional analysis, and mathematical physics. All his life he was interested in the connections of mathematics to physics, which, inter alia, to reflected in his book The Mathematical Foundations of Quantum Mechanics, 1963. 1949 (Duke Mathematical Journal Bd.16, S.313 ) he interpreted the Stone -von Neumann theorem ( about the uniqueness of the operators in Hilbert spaces which satisfy the Heisenberg commutation relations ) as a theorem on continuous unitary representations by operators in Hilbert spaces. He developed the theory ( by a closed subgroup ) Induced representations of locally compact groups, which he characterized by its Impritivitäts criterion.
According to him, the set of Mackey - Arens ( and Mackey topologies ) and the Banach - Mackey are named.
Mackey was a member of the National Academy of Sciences of the United States, the American Academy of Arts and Sciences and the American Philosophical Society. 1964/5 he was vice president of the American Mathematical Society. In 1975 he received the Leroy P. Steele Prize of the American Mathematical Society. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Ergodicity in the theory of group representations ).
He was married and had a daughter.
Among his students David Mumford, Caroline Series, Andrew Gleason, Calvin Moore and Richard Palais.
Writings
- Mackey Mathematical foundations of quantum mechanics, Benjamin, New York 1963
- Idem Mathematical problems of relativistic physics, 1967
- Idem Induced representations of groups and quantum mechanics, 1968
- Idem The theory of unitary group representations, University of Chicago Press 1955, 1976
- Idem Unitary group representations in physics, probability and number theory, Benjamin 1978 ( of lectures in Oxford)
- Idem Ergodic theory and its Significance in statistical mechanics and probability theory, Advances in Mathematics, Bd.12, 1974, 178-268 ( he was awarded the Steele Prize of the AMS)
- Idem Harmonic analysis as the exploitation of symmetry - a historical survey, Bulletin of the American Mathematical Society, New Series, Vol.3, 1980, No.1, S.543 -698 (online here )
- Idem Infinite dimensional group representations, Bulletin of the American Mathematical Society, Bd.69, 1963, S.628 -686