Frigyes Riesz | |
---|---|

Born | |

Died | 28 February 1956 76) | (aged

Citizenship | Hungarian |

Known for | functional analysis integral equations ergodic theory Riesz representation theorem Riesz–Fischer theorem Riesz space Hardy space L space ^{p}Riesz's lemma Radon–Riesz property proximity space F. and M. Riesz 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 spelled as Frederic;^{ [1] } 22 January 1880 – 28 February 1956) was a Hungarian ^{ [2] }^{ [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.^{ [2] } He also made many contributions to other areas including ergodic theory, topology ^{ [6] } and he gave an elementary proof of the mean ergodic theorem.

Riesz founded the Acta Scientiarum Mathematicarum journal together with Alfréd Haar.

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] }

- Riesz, Frigyes; Szőkefalvi-Nagy, Béla (1990) [1955].
*Functional Analysis*. New York: Dover Publications. ISBN 978-0-486-66289-3.

**Functional analysis** is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations.

**Stefan Banach** was a Polish mathematician who is generally considered one of the world's most important and influential 20th-century mathematicians. He was the founder of modern functional analysis, and an original member of the Lwów School of Mathematics. His major work was the 1932 book, *Théorie des opérations linéaires*, the first monograph on the general theory of functional analysis.

**Errett Albert Bishop** was an American mathematician known for his work on analysis. He expanded constructive analysis in his 1967 *Foundations of Constructive Analysis*, where he proved most of the important theorems in real analysis by constructive methods.

**Alfréd Haar** was a Hungarian mathematician. In 1904 he began to study at the University of Göttingen. His doctorate was supervised by David Hilbert. The Haar measure, Haar wavelet, and Haar transform are named in his honor. Between 1912 and 1919 he taught at Franz Joseph University in Kolozsvár. Together with Frigyes Riesz, he made the University of Szeged a centre of mathematics. He also founded the Acta Scientiarum Mathematicarum journal together with Riesz.

**Alfréd Rényi** was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory.

**Marcel Riesz** was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras. He spent most of his career in Lund (Sweden).

**László Kalmár** was a Hungarian mathematician and Professor at the University of Szeged. Kalmár is considered the founder of mathematical logic and theoretical computer science in Hungary.

**Lipót Fejér** was a Hungarian mathematician of Jewish heritage. Fejér was born **Leopold Weisz**, and changed to the Hungarian name Fejér around 1900.

**Raymond Louis Wilder** was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests.

**Hing Tong** was a leading American mathematician. He is well known for providing the original proof of the Katetov–Tong insertion theorem.

**Béla Szőkefalvi-Nagy**[beːlɒ søːkɛfɒlvi nɒɟ] was a Hungarian mathematician. His father, Gyula Szőkefalvi-Nagy was also a famed mathematician. Szőkefalvi-Nagy collaborated with Alfréd Haar and Frigyes Riesz, founders of the Szegedian school of mathematics. He contributed to the theory of Fourier series and approximation theory. His most important achievements were made in functional analysis, especially, in the theory of Hilbert space operators. He was editor-in-chief of the *Zentralblatt für Mathematik*, the *Acta Scientiarum Mathematicarum*, and the *Analysis Mathematica*. He was awarded the Kossuth Prize in 1953, along with his co-author F. Riesz, for his book *Leçons d'analyse fonctionnelle.* He was awarded the Lomonosov Medal in 1979. The Béla Szőkefalvi-Nagy Medal honoring his memory is awarded yearly by Bolyai Institute.

**Børge Christian Jessen** was a Danish mathematician best known for his work in analysis, specifically on the Riemann zeta function, and in geometry, specifically on Hilbert's third problem.

**Bolyai Institute** is the mathematics institute of the Faculty of Sciences of the University of Szeged, named after the Hungarian mathematicians, Farkas Bolyai, and his son János Bolyai, the co-discoverer of non-Euclidean geometry. Its director is László Zádori. Among the former members of the institute are Frigyes Riesz, Alfréd Haar, Rudolf Ortvay, Tibor Radó, Béla Szőkefalvi-Nagy, László Kalmár, Géza Fodor.

**Otto Albin Frostman** was a Swedish mathematician, known for his work in potential theory and complex analysis.

**William Frederick Eberlein** was an American mathematician, specializing in mathematical analysis and mathematical physics.

**Edgar Raymond Lorch** was a Swiss American mathematician. Described by *The New York Times* as "a leader in the development of modern mathematics theory", he was a professor of mathematics at Columbia University. He contributed to the fields general topology, especially metrizable and Baire spaces, group theory of permutation groups and functional analysis, especially spectral theory, convexity in Hilbert spaces and normed rings.

**Extension theorem** may refer to:

**F. Riesz's theorem** is an important theorem in functional analysis that states that a Hausdorff topological vector space (TVS) is finite-dimensional if and only if it is locally compact. The theorem and its consequences are used ubiquitously in functional analysis, often used without being explicitly mentioned.

**John Michael Horvath** was a Hungarian-American mathematician noted for his contributions to analysis especially in functional analysis and distribution theory.

- ↑ 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. - 1 2 Eberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 1990
- ↑ Calendar of Historical Events, Births, Holidays and Observances
- 1 2 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 - ↑
*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.

- Media related to Frigyes Riesz at Wikimedia Commons
- Frigyes Riesz at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Frigyes Riesz",
*MacTutor History of Mathematics archive*, University of St Andrews - Hersh, Reuben; John-Steiner, Vera (1993). "A Visit to Hungarian Mathematics" (PDF).
*Mathematical Intelligencer*.**15**(2): 13–26. doi:10.1007/bf03024187. S2CID 122827181.

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.