Henry Helson

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Henry Helson (1988)

Henry Berge Helson (born June 2, 1927 in Lawrence , Kansas ; † January 10, 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 he obtained his bachelor's degree in 1947 , before visiting European universities in 1947/48 (London, Paris, Prague, Vienna, Warsaw, Breslau with Edward Marczewski ). At the beginning of 1950 he received his doctorate with Lynn Loomis ( Fourier transforms and spectral synthesis on locally compact abelian groups ). He turned down an offer from UCLA because as a Quaker in the McCarthy era he did not want to take the required oath. In 1950/51 he was a lecturer at Uppsala University with Arne Beurling , whose lecture at Harvard he had attended in 1948 and which had a strong influence on him. He also attended the University of Nancy, where a strong group of functional analysts (and Bourbakists ) was active: Laurent Schwartz , Jean Dieudonné , Roger Godement and Alexander Grothendieck . 1951/52 he was an 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 a professor and retired in 1992. In 1957 he became a Sloan Research Fellow . He died of cancer.

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

In 1954 he introduced Helson sets as closed subsets of the circle on which every continuous function has a representation as an absolutely convergent Fourier series. In 1954 he proved a conjecture by Hugo Steinhaus (if the partial sums of a Fourier series are not negative, the Fourier coefficients converge to zero) and also a tightening of the conjecture.

With David Lowdenslager he generalized Beurling's theorem on invariant subspaces. Most influential were her work on generalizing harmonic analysis (and related Hardy spaces) to compact Abelian groups. The theory also had application to stochastic processes.

He also applied Fourier analysis to number theory.

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

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

Fonts

In addition to the works cited in the footnotes (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 opérant dans les algebres de transíormées de Fourier de suites ou de fonctions sommables . CR Acad. Science. Paris 247, 626-628 (1958)
  • with Kahane, Yitzhak Katznelson , Walter Rudin The functions which operate on Fourier transforms , Acta Mathematica, Volume 102, 1959, pp. 135-157

Web links

Individual evidence

  1. ↑ Helson published his memoirs as Mathematics in Poland after the war , Notices AMS 1997, issue 2, pdf
  2. ^ Mathematics Genealogy Project
  3. ↑ Helson Fourier transforms on perfect sets , Studia Math., Volume 14, 1954, pp. 209-213
  4. ↑ Helson Solution of a problem of Steinhaus , Proc. Nat. Acad., Vol. 40, 1954, pp. 205-208
  5. ↑ Helson, Lowdenslager Invariant Subspaces , Proc. Int. Symp. Linear Spaces, Jerusalem 1960, Macmillan 1961, 251-262
  6. ↑ Helson, Lowdenslager Prediction theory and Fourier series in several variables , Acta Mathematica, Volume 99, 1958, pp. 165-202, Part 2 Acta Mathematica, Volume 106, 1961, pp. 175-213
  7. ↑ Your theory is also presented in Kenneth Hoffman Banach Spaces of Analytic Functions , Prentice-Hall 1962
  8. ↑ Helson, Lowdenslager Vector valued processes , Proc. 2. Berkeley Symp. Math. Statistics and Probability, University of California Press 1961, Vol. 2, 203-212
  9. ↑ Helson, Jean-Pierre Kahane A Fourier method in diophantine problems , J. Analyze Math., 16 (1965), 245-226
personal data
SURNAME Helson, Henry
ALTERNATIVE NAMES Helson, Henry Berge (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 2, 1927
PLACE OF BIRTH Lawrence , Kansas
DATE OF DEATH January 10, 2010