Henry Helson

Henry Helson

Henry Berge Helson (June 2, 1927 – January 10, 2010) was an American mathematician at the University of California at Berkeley who worked on analysis.

Helson sets

If G is an infinite, nondiscrete, locally compact group, 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 A(G) in the group G.^[1] Helson was the first to prove that there exist perfect Helson sets for the case of the group consisting of the real line.^[2][3]

Legacy

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

Selected works

• "Proof of a conjecture of Steinhaus". Proc Natl Acad Sci U S A 40 (3): 205–208. March 1954. doi:10.1073/pnas.40.3.205. PMC 527972. PMID 16589456.
• "Conjugate series and a theorem of Paley". Pacific J. Math. 8 (3): 437–446. 1958. doi:10.2140/pjm.1958.8.437. MR 0098952.
• with David Lowdenslager: "Prediction theory and Fourier series of several complex variables". Acta Math. 99: 165–202. 1958. doi:10.1007/bf02392425. MR 97688.
• "Conjugate series in several variables". Pacific J. Math. 9 (2): 513–523. 1959. doi:10.2140/pjm.1959.9.513. MR 0107777.
• with David Lowdenslager: "Prediction theory and Fourier series of several complex variables. II". Acta Math. 106: 175–213. 1961. doi:10.1007/bf02545786. MR 0176287.
• Lectures on invariant subspaces. New York: Academic Press. 1964.
• Harmonic Analysis. Reading, Mass.: Addison-Wesley. 1983; rev. 2nd edn, 1995, publ. Hindustan Book Agency and Helson Publishing Co.^[4]
• with Farhad Zabihi: "A geometric problem in function theory". Illinois J. Math. 51 (3): 1027–1034. 2007. MR 2379736.

References

1. Dunkl, Charles F.; Ramirez, Donald E. (1972). "Helson sets in compact and locally compact groups" (PDF). Michigan Math. J. 19 (1): 65–69. doi:10.1307/mmj/1029000799.
2. Rudin, Walter (1960). "Fourier-Stieltjes transforms of measures on independent sets" (PDF). Bull. Amer. Math. Soc. 66 (3): 199–202. doi:10.1090/s0002-9904-1960-10433-8.
3. Helson, Henry (1954). "Fourier transforms on perfect sets". Studia Math. 14: 209–213.
4. Cooke, Roger (Oct 1996). "Book review of Harmonic Analysis, 2nd edn by Henry Helson". Bull. Amer. Math. Soc. (N.S.) 3 (4): 505–508. doi:10.1090/S0273-0979-96-00682-9.

• Sarason, Donald, ed. (2011), "A tribute to Henry Helson", Notices of the American Mathematical Society 58 (2): 274–288, ISSN 0002-9920, MR 2768120
• Henry Helson at the Mathematics Genealogy Project