Henry Berge Helson (June 2, 1927 – January 10, 2010) was an American mathematician at the

University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...

who worked on analysis.

Education and career

Helson received his bachelor's degree from Harvard University in 1947. With the support of a Harvard travelling fellowship, he spent the academic year 1947–1948 in Europe; he visited London, Paris, Prague, and Vienna, but spent most of his time in Warsaw and then from spring 1948 in Wroclaw, where he worked with Marczewski. Helson received his Ph.D. in 1950 from Harvard with supervisor

Lynn Loomis __NOTOC__ Lynn Harold Loomis (25 April 1915 – 9 June 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality. Loomis received his PhD in 1942 from Harvard Universit ...

and then spent the academic year 1950–1951 primarily in Uppsala working with Beurling but with frequent trips elsewhere in Europe. He became in 1951 an instructor and then an assistant professor at Yale University. He became in 1955 an assistant professor, in 1958 an associate professor, and in 1961 a full professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, retiring there as professor emeritus in 1993. In 1970 he was an Invited Speaker at the ICM in Nice.

Helson sets

If G is an infinite, nondiscrete,

locally compact group In mathematics, a locally compact group is a topological group ''G'' for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are lo ...

, then a Helson set is defined to be a compact set P in G such that every continuous function on P can be extended to a function in the

Fourier algebra Fourier and related algebras occur naturally in the harmonic analysis of locally compact groups. They play an important role in the duality theories of these groups. The Fourier–Stieltjes algebra and the Fourier–Stieltjes transform on the Four ...

A(G) in the group G. Helson was the first to prove that there exist perfect Helson sets for the case of the group consisting of the real line.

Legacy

Helson founded the mathematics-specialty publishing company Berkeley Books. Upon his death he was survived by his wife Ravenna Helson, a renowned personality psychologist, their daughter, two sons, and three grandchildren. His doctoral students include Frank Forelli and Udai Tewari.

Selected works

* * * with David Lowdenslager: * * with David Lowdenslager: * * * with Farhad Zabihi:

References

* * {{DEFAULTSORT:Helson, Henry 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni Institute for Advanced Study visiting scholars Mathematical analysts 1927 births 2010 deaths University of California, Berkeley College of Letters and Science faculty