Mathematician:Frigyes Riesz

Mathematician

Hungarian mathematician who developed the field of functional analysis.

Gave an elementary proof of the Mean Ergodic Theorem.

Elder brother of the mathematician Marcel Riesz.

Nationality

Hungarian

History

• Born: 22 Jan 1880, Györ, Austria-Hungary (now Hungary)
• Died: 28 Feb 1956, Budapest, Hungary

Theorems and Definitions

• Riesz's Convergence Theorem
• Riesz's Lemma
• Riesz Representation Theorem (Hilbert Spaces)
• Riesz Representation Theorem (for duals of function spaces $\map {C_c} X$ and $\map {C_0} X$)
• Riesz-Markov-Kakutani Representation Theorem (with Andrey Andreyevich Markov Jr. and Shizuo Kakutani)

• F. and M. Riesz Theorem (with Marcel Riesz)
• Riesz-Fischer Theorem (independently of Ernst Sigismund Fischer)

• Riesz Functional Calculus
• Riesz Space
• Radon-Riesz Property (with Johann Karl August Radon)

• Proximity Space

Results named for Frigyes Riesz can be found here.

Definitions of concepts named for Frigyes Riesz can be found here.

Publications

• 1907: Sur une espèce de géométrie analytiques des systèmes de fonctions sommables
• 1907: Sur les systèmes orthogonaux de fonctions
• 1909: Sur les opérations fonctionelles linéaires
• 1916: Über die Randwerte einer analytischen Funktion (with Marcel Riesz)
• 1928: Sur la décomposition des opérations fonctionelles linéaires
• 1953: Leçons d'analyse fonctionnelle (with Béla Sz.-Nagy)
• 1988: Funkcionálanalízis (with Béla Sz.-Nagy)
• 1990: Functional Analysis (with Béla Sz.-Nagy; translated by Leo F. Boron)

Sources

• John J. O'Connor and Edmund F. Robertson: "Frigyes Riesz": MacTutor History of Mathematics archive