# Frigyes Riesz

Frigyes Riesz

Frigyes Riesz [ ˈfriɟɛʃ ri: s ] (first name also German Friedrich or French Frédéric , born January 22, 1880 in Győr ; † February 28, 1956 in Budapest ) was a Hungarian mathematician who made significant contributions to functional analysis.

## Life

Frigyes Riesz was the older brother of Marcel Riesz . He studied in Budapest, Göttingen and Zurich and received his doctorate in 1902 at the Eötvös-Loránd University in Budapest. In 1911 he was appointed to a chair at the University of Kolozsvár (Eng. Cluj-Napoca , Transylvania ). When Kolozsvár (now Cluj-Napoca , Romania ) became Romanian with the Peace of Trianon in 1920, the university was moved to Szeged . Together with Alfréd Haar , Riesz founded the János Bolyai Institute for Mathematics in Szeged in 1922 . In 1945 he followed a call to Budapest.

Riesz published in Hungarian, German and French; his writings are praised for their exceptional clarity.

Riesz was one of the founders of functional analysis . In 1907 he proved the day for him and Ernst Fischer named set on the Fourier analysis of Hilbert spaces , on the equivalence of Matrizen- and wave mechanics is based. In addition, the Radon-Riesz theorem is named after him, which specifies criteria under which the convergence in the p-th mean and the weak convergence are${\ displaystyle {\ mathcal {L}} ^ {p}}$ equivalent, as well as the Riesz-Markow representation theorem , which characterizes the positive linear forms on certain function spaces by means of measures .

In his honor, vector spaces with a suitable association structure are called Riesz spaces .

In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (Sur l'existence de la dérivée des fonctions d'une variable réelle et des fonctions d'intervalle). In 1948 he was accepted as a corresponding member of the Académie des sciences in Paris. In 1954 he became a corresponding member of the Bavarian Academy of Sciences .

## literature

• Laura Regina Rodríguez Hernández: Friedrich Riesz 'contributions to the development of the modern mathematical concept of abstract spaces. Syntheses of intellectual cultures in Hungary, France and Germany. Dissertation, University of Mainz 2006 ( full text ).
• Erwin Kreyszig: Friedrich Riesz as a pioneer of functional analysis. In: Elements of Mathematics. Vol. 45, No. 5, 1990, pp. 117–144, (digitized version of the Göttingen digitization center.)