Henry Helson

Henry Helson mountains ( born June 2, 1927 in Lawrence, Kansas; † 10 January 2010) was an American mathematician who dealt with ( commutative ) harmonic analysis and function theory.

Helson was the son of a professor of psychology at Bryn Mawr College. He studied at Harvard University, where in 1947 he took his bachelor's degree before he visited (London, Paris, Prague, Vienna, Warsaw, Wroclaw in Edward Marczewski ) 1947/48 European universities. In early 1950, he received his doctorate in Lynn Loomis (Fourier transforms and spectral synthesis on locally compact abelian groups). A service of UCLA, he lashed out because he did not want to make in the McCarthy era as a Quaker the required mandatory oath. 1950/51 he was a lecturer at the University of Uppsala in Arne Beurling, whose lecture at Harvard in 1948, he had visited and who influenced him greatly. He also attended the University of Nancy, where a strong group of functional analysts ( and Bourbakisten ) was active: Laurent Schwartz, Jean Dieudonné, Roger Godement and Alexander Grothendieck. 1951/52, he was instructor at Yale University. In 1954 he became an Assistant Professor at Yale, and in 1955 at the University of California, Berkeley, where he became professor emeritus in 1992. He died of cancer.

In 1960 he was at the Institute for Advanced Study. He was a visiting professor in France (Montpellier, Marseille, Orsay ), Bonn, Florence, Ghana, India and Sweden. He is known for important contributions to harmonic analysis of locally compact abelian groups.

In 1954, he led a Helson sets as closed subsets of the circle on which every continuous function has a representation as absolutely convergent Fourier series. In 1954 he proved a conjecture of Hugo Steinhaus (if the partial sums of a Fourier series are non-negative, the Fourier coefficients converge to zero ) and also a tightening of the conjecture.

With David Lowdenslager he generalized the theorem on invariant subspaces of Beurling At their most influential work on the generalization of harmonic analysis ( and associated Hardy spaces ) were on compact abelian groups, the theory also had application to stochastic processes.

He used also Fourier analysis in number theory.

In 1970 he was invited speaker at the ICM in Nice ( Cocycles in Harmonic Analysis).

Helson was married to the psychologist Ravenna Helson since 1954 and had three children. In his spare time he played the violin and viola. He founded his own small publishing house for books on mathematics, Berkeley Books.

Writings

In addition to the references cited in the footnotes work (selection):

  • Harmonic Analysis, Addison -Wesley 1993
  • Lectures on invariant subspaces, Academic Press 1964
  • The spectral theorem, Springer Verlag 1986
  • Analyticity on compact abelian groups, in JH Williamson Algebras in Analysis, Academic Press, 1975, 1-62
  • Note on harmonic functions, Proc. AMS, 4, 1953, 686-691
  • On a theorem of Szegö, Proc. AMS, 6, 1955, 235-242
  • Isomorphisms of abelian group algebras, Arkiv Math, 2, 1952, 475-487
  • With Beurling Fourier - Stieltjes transforms with bounded powers, Math Scand. , 1, 1953, pp. 120-126
  • With Jean -Pierre Kahane Sur les fonctions dans les operant algebres transíormées de de de Fourier suites ou de fonctions sommables. C. R. Acad. Science. Paris 247, 626-628 (1958 )
  • With Kahane, Yitzhak Katznelson, Walter Rudin The functions operate on Which Fourier transforms, Acta Mathematica, Volume 102, 1959, pp. 135-157 < / ref >
Lawrence (Kansas) Complex analysis Locally compact group Jean-Pierre Kahane Integrated Authority File
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