Frigyes Riesz

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Frigyes Riesz
Born(1880-01-22)22 January 1880
Died28 February 1956(1956-02-28) (aged 76)
Known forFunctional analysis
Integral equations
Ergodic theory
Weak topology
Hardy space
Lp space
Proximity space
Denjoy–Riesz theorem
Herglotz–Riesz representation theorem
Riesz space
Riesz rearrangement inequality
Riesz's lemma
Riesz representation theorem
Riesz–Fischer theorem
Riesz projector
Radon–Riesz property
F. and M. Riesz theorem
F. Riesz's theorem
Riesz–Markov–Kakutani representation theorem
Scientific career
Doctoral advisorGyula Vályi
Doctoral studentsJános Aczél
Steven Gaal
John Horvath
Tibor Radó
Alfréd Rényi

Frigyes Riesz (Hungarian: Riesz Frigyes, pronounced [ˈriːs ˈfriɟɛʃ], sometimes spelled as Frederic;[1] 22 January 1880 – 28 February 1956)[2] was a Hungarian[3] mathematician who made fundamental contributions to functional analysis, as did his younger brother Marcel Riesz.

Life and career[edit]

He was born into a Jewish family in Győr, Austria-Hungary and died in Budapest, Hungary. Between 1911 and 1919 he was a professor at the Franz Joseph University in Kolozsvár, Austria-Hungary. The post-WW1 Treaty of Trianon transferred former Austro-Hungarian territory including Kolozsvár to the Kingdom of Romania, whereupon Kolozsvár's name changed to Cluj and the University of Kolozsvár moved to Szeged, Hungary, becoming the University of Szeged.[4] Then, Riesz was the rector and a professor at the University of Szeged, as well as a member of the Hungarian Academy of Sciences.[5] and the Polish Academy of Learning. He was the older brother of the mathematician Marcel Riesz.

Riesz did some of the fundamental work in developing functional analysis and his work has had a number of important applications in physics. He established the spectral theory for bounded symmetric operators in a form very much like that now regarded as standard.[3] He also made many contributions to other areas including ergodic theory, topology[6] and he gave an elementary proof of the mean ergodic theorem.

Together with Alfréd Haar, Riesz founded the Acta Scientiarum Mathematicarum journal.

He had an uncommon method of giving lectures: he entered the lecture hall with an assistant and a docent. The docent then began reading the proper passages from Riesz's handbook and the assistant wrote the appropriate equations on the blackboard—while Riesz himself stood aside, nodding occasionally.[7]

The Swiss-American mathematician Edgar Lorch spent 1934 in Szeged working under Riesz and wrote a reminiscence about his time there, including his collaboration with Riesz.[4]

The corpus of his bibliography was compiled by the mathematician Pál Medgyessy.[8]


  • Riesz, Frederic; Sz.-Nagy, Béla (1990) [1955]. Functional Analysis. Translated by Boron, Leo F. New York: Dover Publications. ISBN 0-486-66289-6. OCLC 21228994.

See also[edit]


  1. ^ W. J. Thron, Frederic Riesz' contributions to the foundations of general topology, in C.E. Aull and R. Lowen (eds.), Handbook of the History of General Topology, Volume 1, 21-29, Kluwer 1997.
  2. ^ O'Connor, John J.; Robertson, Edmund F., "Frigyes Riesz", MacTutor History of Mathematics Archive, University of St Andrews
  3. ^ a b Eberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 1990 [1]
  4. ^ a b Lorch, Edgar R. (1993). Hersh, Rubem (ed.). "Szeged in 1934". Amer. Math. Monthly. 100 (3): 219–230. doi:10.2307/2324453. JSTOR 2324453.
  5. ^ János Horváth: A Panorama of Hungarian Mathematics in the Twentieth Century, Volume 1, Springer, 2006 [2]
  6. ^ Frederic Riesz made significant suggestions as to how the axiomatic foundations of general topology might be formulated... Unfortunately they were generally overlooked at that time and their importance was appreciated only after they were rediscovered much later... He lost interest in General Topology after 1908 and never elaborated any of the promising ideas he had put forward, Thron, cit.
  7. ^ Wróblewski, Andrzej Kajetan (September 2008). "Czyściec, niebo i piekło". Wiedza i Życie: 65.
  8. ^ Pál Medgyessy's entry in Tudósnaptár ("Calendar of Scientists")

External links[edit]