Frigyes Riesz
Born: 22 Jan 1880 in Györ, Austria-Hungary (now Hungary)
Died: 28 Feb 1956 in Budapest, Hungary
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Riesz was a founder of functional analysis and his work has many important applications in physics.
He built on ideas introduced by Fréchet in his dissertation, using Fréchet's ideas of distance to provide a link between Lebesgue's work on real functions and the area of integral equations developed by Hilbert and his student Schmidt.
In 1907 and 1909 Riesz produced representation theorems for functional on quadratic Lebesgue integrable functions and, in the second paper, in terms of a Stieltjes integral. The following year he introduced the space of q-fold Lebesgue integrable functions and so he began the study of normed function spaces, since, for q
3 such spaces are not Hilbert spaces. Riesz introduced the idea of the 'weak convergence' of a sequence of functions {f
(x)}. A satisfactory theory of series of orthonormal functions only became possible after the invention of the Lebesgue integral and this theory was largely the work of Riesz.
Riesz's work of 1910 marks the start of operator theory. In 1918 his work came close to an axiomatic theory for Banach spaces, which were set up axiomatically two years later by Banach in his dissertation.
Riesz was appointed to a chair in Kolozsvár in Hungary (which is now Cluj in Romania) in 1911. In 1922 he became editor of the newly founded journal Acta Scientiarum Mathematicarum which quickly became a major source of mathematics.
In 1945 Riesz was appointed to the chair of mathematics in the University of Budapest.
Many of Riesz's fundamental findings in functional analysis were incorporated with those of Banach. His theorem, now called the Riesz-Fischer theorem, was the mathematical basis for proving that matrix mechanics and wave mechanics were equivalent. This is of fundamental importance in early quantum theory.
Riesz made many contributions to other areas including ergodic theory, orthonormal series and topology.
His book Lecon's d'analyse fonctionnelle is one of the most readable accounts of functional analysis ever written.
References elsewhere in this archive:
Tell me about Riesz's work on topology
Tell me about Riesz's work on quantum theory
References:
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