Frigyes Riesz | |
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Born | |

Died | 28 February 1956 | (aged 76)

Citizenship | Hungarian |

Known for | Functional analysis Integral equations Ergodic theory Weak topology Hardy space L space^{p}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 | |

Fields | Mathematics |

Doctoral advisor | Gyula Vályi |

Doctoral students | János Aczél Steven Gaal John Horvath Tibor Radó Alfréd Rényi |

**Frigyes Riesz** (Hungarian: *Riesz Frigyes*, pronounced [ˈriːs ˈfriɟɛʃ], sometimes known in English and French as **Frederic Riesz**;^{[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.

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.

- Proximity space
- Rising sun lemma
- Denjoy–Riesz theorem
- F. and M. Riesz theorem
- Riesz representation theorem
- Riesz-Fischer theorem
- Riesz groups
- Riesz's lemma
- Riesz projector
- Riesz sequence
- Riesz space
- Radon-Riesz property

**^**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.**^**O'Connor, John J.; Robertson, Edmund F., "Frigyes Riesz",*MacTutor History of Mathematics Archive*, University of St Andrews- ^
^{a}^{b}Eberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 1990 [1] - ^
^{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. **^**János Horváth:*A Panorama of Hungarian Mathematics in the Twentieth Century*, Volume 1, Springer, 2006 [2]**^***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.**^**Wróblewski, Andrzej Kajetan (September 2008). "Czyściec, niebo i piekło".*Wiedza i Życie*: 65.**^**Pál Medgyessy's entry in*Tudósnaptár*("Calendar of Scientists")

- Media related to Frigyes Riesz at Wikimedia Commons
- Frigyes Riesz at the Mathematics Genealogy Project
- Hersh, Reuben; John-Steiner, Vera (1993). "A Visit to Hungarian Mathematics" (PDF).
*Mathematical Intelligencer*.**15**(2): 13–26. doi:10.1007/bf03024187. S2CID 122827181. Archived from the original (PDF) on 27 June 2013. Retrieved 22 August 2012.

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