Friedrich Riesz als Wegbereiter der Funktionalanalysis. (Friedrich Riesz -- pioneer of functional analysis)
type: Item
instance of: scholarly article
title: Friedrich Riesz als Wegbereiter der Funktionalanalysis. (Friedrich Riesz -- pioneer of functional analysis)
zbMATH Open document ID: 0723.01009
published in: Elemente der Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141489
review text: The author provides a short but a fairly detailed mathematical survey of Friedrich Riesz's contributions to functional analysis. Starting off with a brief biographical essay on Riesz and a graph indicating the periods during which Riesz worked in various fields (topology, measure and integration, function theory, subharmonic functions and ergodic theory, as well as functional analysis), he then proceeds to describe specific contributions: the Riesz-Fisher theorem, \(L^ p\)-spaces and their functionals, the Riesz form of Hilbert spectral theory, compact linear operators and Riesz spaces. The author points out Riesz's special qualities: the long period over which he made these contributions (1907 to 1940), the depth of his work and his clear exposition of it, along with the fact that Riesz had had contact with both the Göttingen school (Hilbert and his followers) and Paris (Hadamard, Lebesgue and Fréchet, among others).
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 46-03
zbMATH DE Number: 4191580
zbMATH Keywords: spectral theory
zbMATH Keywords: Hilbert space. topology
zbMATH Keywords: measure
zbMATH Keywords: integration
zbMATH Keywords: function theory
zbMATH Keywords: subharmonic functions
zbMATH Keywords: ergodic theory
zbMATH Keywords: Riesz-Fisher theorem
author: Erwin O. Kreyszig
reviewed by: Gerald L. Alexanderson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4191580