Marshall Harvey Stone

Marshall Harvey Stone ( born April 8, 1903 in New York City; † January 9, 1989 in Madras, India) was an American mathematician who mainly focused on functional analysis.

Life and work

Stone attended school in Englewood (New Jersey) and studied from 1919 at Harvard. After Bachelor degree in Law, he switched to mathematics, what was done to him palatable by a probationary period as an instructor 1922/23. In 1926 he received his doctorate at George David Birkhoff with a thesis on ordinary differential equations and development based on orthogonal function systems. In 1925 he became an instructor at Columbia University and in 1927 at Harvard, where he became Associate Professor in 1928. After a period from 1931 to 1933 as an associate professor at Yale, he was Associate Professor in 1933 and Professor in 1937 at Harvard. From 1928 he worked on self-adjoint operators in Hilbert spaces, what 1932 his book appeared linear transformation in Hilbert Space and their Applications to Analysis. He even coined the term self-adjoint operator. In 1930 he published in the Proceedings of the National Academy of Sciences the famous Stone - von Neumann theorem (which was not included for reasons of space in his monograph of 1932).

Then he dealt with spectral theory and there problems resulting from the group theoretical treatment of quantum mechanics by Hermann Weyl. In 1934, he published papers on Boolean algebras which contain the Stone - Čech compactification. He also extended the approximation of continuous functions by polynomials by Karl Weierstrass at the rate of Stone - Weierstrass. During World War II he worked 1942/43, for the Office of Naval Operations, and then for the General Staff. In 1946 he moved to the University of Chicago, where he became a faculty chairman. He particularly wanted to lift the state of research and made ​​sure that André Weil, Saunders Mac Lane, Antoni Zygmund and Shiing - Shen Chern came to Chicago. In 1952 he gave up the presidency of the faculty in favor of Mac Lane, but remained until his retirement in 1968 in Chicago. After that, he was a professor at the University of Massachusetts to 1980 ( from 1973 only part-time).

Marshall Stone was in the 1950s, a vigorous proponent of the Bourbaki flow ( among other reasons, because he got to the University ) and connected to the new mathematics.

In 1938 he was elected to the National Academy of Sciences. 1943/44, he was president of the American Mathematical Society. In 1956 he was Gibbs Lectureer. From 1952 to 1954 he was president of the International Mathematical Union. From 1961 to 1967 he was president of the International Committee of Mathematical Instruction.

Stone went willingly and was at the time of his death on a trip to India.

Eponym

Among the results that bear Stones names include

  • The set of Stone -von Neumann
  • The set of Stone - Weierstrass
  • The Stone - Čech compactification
  • Stones representation theorem for Boolean algebras
  • The set of Stone - Tukey (along with John W. Tukey )
  • The set of Daniell - Stone ( supplemented the set of Percy John Daniell in 1948 to an important prerequisite )
  • The set of Stone

Family

Stones father was the lawyer Harlan Fiske Stone, who was 21 years Judge of the U.S. Supreme Court, including 1941-1946 as Chief Justice; his mother was Agnes Harvey Stone (1873 - 1958).

Stone was married twice. From the first marriage from 1927 to 1962 produced three children.

Writings

  • Linear transformations in Hilbert space and their applications to analysis, American Mathematical Society 1932
  • Theory of real functions, Ann Arbor 1940
  • Linear Transformations in Hilbert Space. III. Operational Methods and Group Theory, Proceedings of the National Academy of Sciences (USA), Volume 16, 1930, pp. 172-175
  • On one- parameter unitary groups in Hilbert space, Annals of Mathematics, Volume 33, 1932, pp. 643-648
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