Friedrich Riesz als Wegbereiter der Funktionalanalysis. (Friedrich Riesz -- pioneer of functional analysis) (Q757331)

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).