George Mackey

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George Mackey

George Whitelaw Mackey (born February 1, 1916 in St. Louis , † March 15, 2006 in Belmont (Massachusetts) ) was an American mathematician . George Mackey grew up in Houston, Texas, where he began studying physics, chemical engineering, and mathematics at the Rice Institute. He continued his mathematics studies at Harvard University , where he received his doctorate in 1942 under Marshall Harvey Stone , with a thesis on locally convex topologies in vector spaces (introduction of the Mackey topology). After a stopover at the Illinois Institute of Technology , at Caltech and at the Institute for Advanced Study (1941) in Princeton , he returned to Harvard as an instructor in 1943 and stayed there - from 1956 as a professor (from 1969 to Landon T. Clay Professor for Mathematics ) - until his retirement in 1985. his main fields were representation theory , ergodic theory , functional analysis and mathematical physics . Throughout his life he was interested in the connections between mathematics and physics. a. in his 1963 book The Mathematical foundations of Quantum Mechanics . In 1949 (Duke Mathematical Journal Vol. 16, p. 313) he interpreted the Stone-von Neumann theorem (about the uniqueness of the operators in Hilbert spaces that satisfy Heisenberg's commutation relations) as the theorem about continuous unitary representations by operators in Hilbert spaces. He developed the theory (by a closed subgroup) of induced representations of locally compact groups , which he characterized by his impritivity criterion .

The Mackey-Arens theorem (and Mackey topologies), the Mackey criterion and the Banach-Mackey theorem are named after him.

Mackey was a member of the US National Academy of Sciences , the American Philosophical Society and, since 1953, the American Academy of Arts and Sciences . In 1964/5 he was Vice President of the American Mathematical Society . In 1975 he received the Leroy P. Steele Prize from 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.

His students include David Mumford , Caroline Series , Andrew Gleason , Calvin Moore , Paul Chernoff, and Richard Palais .

Fonts

  • Mackey Mathematical foundations of quantum mechanics , Benjamin, New York 1963
  • ders. Mathematical problems of relativistic physics , 1967
  • ders. Induced representations of groups and quantum mechanics , 1968
  • ders. The theory of unitary group representations , University of Chicago Press 1955, 1976
  • ders.Unitary group representations in physics, probability and number theory , Benjamin 1978 (from lectures in Oxford)
  • ders. Ergodic theory and its significance in statistical mechanics and probability theory , Advances in mathematics, Vol. 12, 1974, 178–268 (for this he received the Steele Prize from the AMS)
  • ders. Harmonic analysis as the exploitation of symmetry - a historical survey , Bulletin of the American Mathematical Society, New Series, Vol. 3, 1980, No. 1, pp. 543–698 (online here [2] )
  • ders. Infinite dimensional group representations , Bulletin of the American Mathematical Society, Vol. 69, 1963, pp. 628-686

Web links

Commons : George Mackey  - Collection of Images, Videos and Audio Files

Individual evidence

  1. ^ Members of the American Academy. Listed by election year, 1950-1999 ( [1] ). Retrieved September 23, 2015
personal data
SURNAME Mackey, George
ALTERNATIVE NAMES Mackey, George Whitelaw (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH February 1, 1916
PLACE OF BIRTH St. Louis , United States
DATE OF DEATH March 15, 2006
Place of death Belmont (Massachusetts) United States