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.

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[1] 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, retiring there as professor emeritus in 1993. In 1970 he was an Invited Speaker at the ICM in Nice.[2]

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.[3] Helson was the first to prove that there exist perfect Helson sets for the case of the group consisting of the real line.[4][5]

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

  • Helson, H. (March 1954). "Proof of a conjecture of Steinhaus". Proc Natl Acad Sci U S A. 40 (3): 205–208. Bibcode:1954PNAS...40..205H. doi:10.1073/pnas.40.3.205. PMC 527972. PMID 16589456.
  • Helson, Henry (1958). "Conjugate series and a theorem of Paley". Pacific J. Math. 8 (3): 437–446. 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 0097688.
  • Helson, Henry (1959). "Conjugate series in several variables". Pacific J. Math. 9 (2): 513–523. 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.[6]
  • Harmonic Analysis. Reading, Mass.: Addison-Wesley. 1983; rev. 2nd edn, 1995, publ. Hindustan Book Agency and Helson Publishing Co.{{cite book}}: CS1 maint: postscript (link)[7]
  • with Farhad Zabihi: Helson, Henry; Zabihi, Farhad (2007). "A geometric problem in function theory". Illinois J. Math. 51 (3): 1027–1034. doi:10.1215/ijm/1258131116. MR 2379736.

References

  1. ^ Henry Helson at the Mathematics Genealogy Project
  2. ^ Helson, Henry. "Cocycles in harmonic analysis." Archived 2016-09-24 at the Wayback Machine Actes du congreés international des matheèmaticiens (1970).
  3. ^ 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.
  4. ^ 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.
  5. ^ Helson, Henry (1954). "Fourier transforms on perfect sets". Studia Math. 14 (2): 209–213. doi:10.4064/sm-14-2-209-213.
  6. ^ Halmos, P. R. (1965). "Book review of Lectures on invariant subspaces by Henry Helson". Bull. Amer. Math. Soc. 71 (3): 490–494. doi:10.1090/S0002-9904-1965-11294-0. MR 1566346.
  7. ^ 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.

Read other articles:

Venerida

Venerida Venus verrucosa Klasifikasi ilmiah Domain: Eukaryota Kerajaan: Animalia Filum: Mollusca Kelas: Bivalvia Infrakelas: Heteroconchia Superordo: Imparidentia Ordo: VeneridaGray, 1854 Famili Lihat teks Sinonim Veneroida Venerida (sinonim: Veneroida) adalah ordo bivalvia yang sebagian besarnya terdiri dari kerang air asin, dan sebagian kecil kerang air tawar. Ordo ini mencakup banyak kelompok yang sudah dikenal seperti banyak kerang yang bernilai untuk makanan, dan sejumlah kerang air taw...

 

F.C. Legnago Salus S.S.D.

Legnago SalusLogo FC legnano SalusNama lengkapFootball Club Legnago Salus Società Sportiva Dilettantistica a r.l.Berdiri19212011 (refounded)StadionStadio Mario Sandrini,Legnago, Italy(Kapasitas: 1,200)Ketua Davide VenturatoManajer Massimo DonatiLigaSerie C/A2022-2023Serie D/C, 2rd Kostum kandang Kostum tandang Football Club Legnago Salus Società Sportiva Dilettantistica (dulu bernama Associazione Calcio Legnago Salus) adalah sebuah klub sepak bola Italia dari kota Legnago, Veneto. Saat ini ...

 

Yash Chopra

Yash ChopraYash Chopra di Peluncuran Proyek Charcoal yang dibuat oleh Suzanne RoshanLahirYash Raj Chopra(1932-09-27)27 September 1932Lahore, Punjab, India BritaniaMeninggal21 Oktober 2012(2012-10-21) (umur 80)Mumbai, Maharashtra, IndiaSebab meninggalDeman berdarahKebangsaanIndiaPekerjaanSutradara, Script Writer, ProduserTahun aktif1959–2012OrganisasiYash Raj FilmsSuami/istriPamela Yash ChopraAnakAditya ChopraUday ChopraTanda tanganTanda tangan Inggris Yash Chopra Yash Raj Ch...

Fiord

Sognefjord, Norwegia merupakan sebuah fyord terbesar kedua di dunia. Fyord[1] atau teluk ngarai merupakan semacam teluk yang berasal dari lelehan gletser, yaitu tumpukan es yang sangat tebal dan berat.[2] Fyord bisa sangat dalam dan sangat panjang. Fyord banyak ditemukan di negara Skandinavia dan di Amerika Utara, terutama Alaska dan Kanada.[3] Etimologi Istilah fyord dalam bahasa Indonesia diserap dari kata fjord atau fiord dalam bahasa Inggris, dibaca sebagai /ˈfjɔ...

 

Arizona's 19th legislative district

American legislative district Legislative district in Arizona, United States Arizona's 19th legislative districtMap of District 19: Approved January 21, 2022SenatorDavid Gowan (R)House membersGail Griffin (R)Lupe Diaz (R)Registration41.99% Republican24.97% Democratic33.04% OtherDemographics61% White3% Black/African American2% Native American3% Asian29% HispanicPopulation230,476Voting-age population182,745Registered voters146,048 Arizona's 19th legislati...

 

KGPZ-LP

Radio station in Grants Pass, OregonKGPZ-LPGrants Pass, OregonFrequency106.7 MHzProgrammingFormatReligiousOwnershipOwnerSonSong Media(SonSong Media)HistoryFormer call signsKCGP-LP (2005–2022)Technical informationFacility ID133956ClassL1ERP70 wattsHAAT−44.6 meters (−146 ft)Transmitter coordinates42°25′22″N 123°23′57″W / 42.42278°N 123.39917°W / 42.42278; -123.39917 This article relies largely or entirely on a single source. Relevant discussion may...

1998 Himachal Pradesh Legislative Assembly election

Legislative Assembly election in Himachal Pradesh, India 1998 Himachal Pradesh Legislative Assembly election ← 1993 28 February and 3 June 1998 2003 → All 68 seats in the Himachal Pradesh Legislative Assembly35 seats needed for a majorityRegistered3,628,864Turnout71.23%   Majority party Minority party   Leader Prem Kumar Dhumal Virbhadra Singh Party BJP INC Seats before 8 52 Seats won 31 31 Seat change 23 21 Popular vote 995,482 1,110,055 Pe...

 

2nd Brigade Combat Team

2nd Brigade Combat Team or 2 BCT is a designation for modularized brigades of the United States Army. It may refer to: 2nd Brigade Combat Team, 1st Cavalry Division (United States) 2nd Brigade Combat Team, 1st Armored Division (United States) 2nd Brigade Combat Team, 1st Infantry Division (United States) 2nd Brigade Combat Team, 2nd Infantry Division (United States) 2nd Brigade Combat Team, 3rd Infantry Division (United States) 2nd Brigade Combat Team, 4th Infantry Division (United States) 2n...

 

Abbaye de Faremoutiers

Pour les articles homonymes, voir Abbaye Notre-Dame. Abbaye de Faremoutiers Présentation Culte Catholicisme Type Abbaye Début de la construction VIIe siècle Site web http://www.abbayedefaremoutiers.fr/ Géographie Pays France Région Île-de-France Département Seine-et-Marne Ville Faremoutiers Coordonnées 48° 48′ 07″ nord, 2° 59′ 51″ est Géolocalisation sur la carte : Île-de-France Géolocalisation sur la carte : France modifier&#...

土库曼斯坦总统

土库曼斯坦总统土库曼斯坦国徽土库曼斯坦总统旗現任谢尔达尔·别尔德穆哈梅多夫自2022年3月19日官邸阿什哈巴德总统府（Oguzkhan Presidential Palace）機關所在地阿什哈巴德任命者直接选举任期7年，可连选连任首任萨帕尔穆拉特·尼亚佐夫设立1991年10月27日 土库曼斯坦土库曼斯坦政府与政治 国家政府 土库曼斯坦宪法 国旗 国徽 国歌 立法機關（英语：National Council of Turkmenistan） ...

 

All Rise (TV series)

2019 American legal drama television series All RiseGenreLegal dramaBased onCourtroom 302by Steve BogiraDeveloped byGreg SpottiswoodStarring Simone Missick Wilson Bethel Jessica Camacho J. Alex Brinson Ruthie Ann Miles Lindsay Mendez Marg Helgenberger Lindsey Gort Audrey Corsa Reggie Lee ComposerJoey NewmanCountry of originUnited StatesOriginal languageEnglishNo. of seasons3No. of episodes58ProductionExecutive producers Greg Spottiswood Michael M. Robin Leonard Goldstein Sunil Nayar Lydia Woo...

 

COVID-19 Response Acceleration Task Force

Task Force to Handle the Covid-19 Pandemic in Indonesia COVID-19 Response Acceleration Task ForceGugus Tugas Percepatan Penanganan COVID-19Agency overviewFormed13 March 2020 (4 years ago) (2020-03-13)Dissolved20 July 2020 (3 years ago) (2020-07-20)Superseding agencyCOVID-19 Handling and National Economic Recovery Committee [id] (Indonesian: Komite Penanganan COVID-19 dan Pemulihan Ekonomi Nasional[1])Jurisdiction IndonesiaHeadquartersIndon...

Electoral and ethics policy of the Joe Biden administration

Overview of the Biden administration's electoral and ethical policies This article is part of a series aboutJoe Biden Political positions Electoral history Early life and career Eponyms Family Honors Public image U.S. Senator from Delaware Judiciary Committee Bork hearings Thomas hearings 1994 Crime Bill Violence Against Women Act Foreign Relations Committee Elections: 1972 1978 1984 1990 1996 2002 2008 47th Vice President of the United States Transition Tenure Obama administration first inau...

 

Nile University of Nigeria

Private research institution in Nigeria This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Nile University of Nigeria – news · newspapers · books · scholar · JSTOR (October 2015) (Learn how and when to remove this message) Nile University of NigeriaMottoBuild Your Success For A Better SocietyTypePrivateEstablis...

 

J

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (فبراير 2024) Jمعلومات عامةجزء من إخطاطة لاتينيةPolish alphabet (en) أبجدية إنجليزية الرمز .---JulietJ تعديل - تعديل مصدري - تعديل ويك...

Metropolitan Evansville Transit System

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Metropolitan Evansville Transit System – news · newspapers · books · scholar · JSTOR (June 2021) (Learn how and when to remove this message) Metropolitan Evansville Transit SystemA METS Hybrid-Electric busFounded1971Headquarters601 John StreetLocaleEvansville, ...

 

Державна автомобільна інспекція України

Не плутати з державною екологічною інспекцією — органом державної влади в Україні, чиїм завданням є екологічний контроль над природним середовищем. Державна автомобільна інспекція МВС України(ДАІ)     Загальна інформація: Тип: дорожня поліція Юрисдикція:  Укр�...

 

Kanjar Ro

Comics character Kanjar RoKanjar Ro as depicted in his debut appearance in Justice League of America #3 (February 1961); art by Murphy Anderson.Publication informationPublisherDC ComicsFirst appearanceJustice League of America #3 (February 1961)Created byGardner FoxMike SekowskyIn-story informationAlter egoKanjar RoPlace of originDhorTeam affiliationsR.E.B.E.L.S.AbilitiesBasic martial art skills, and possessed high tech weaponry, including a Gamma Gong that renders people motionless. This art...

佐藤佐太郎

佐藤佐太郎 佐藤 佐太郎（さとう さたろう、1909年（明治42年）11月13日 - 1987年（昭和62年）8月8日）は、日本の歌人。日本芸術院会員。妻の佐藤志満も歌人。 岩波書店に入社。短歌に関心を抱き「アララギ」に入会、斎藤茂吉に師事。近代の憂愁をたたえた第一歌集『歩道』(1940年)から、老境を自覚した寂寥感あふれる『星宿』(1983年)まで、新境地を拓き続けた。歌論に�...

 

مقبرة المعلاة

مقبرة المعلاة منظر عام للمقبرة المكان مكة المكرمة البلد  السعودية النوع مقبرة المسلمين ديانات الإسلام بعض الأرقام الموقع على الخريطة تعديل مصدري - تعديل   مقبرة المَعَلاةُ مقبرة للمسلمين عامة لأهل مكة المكرمة منذ عصر ما قبل الإسلام وحتى الوقت الحاضر. تقع في بداية طري...