Marcel Riesz
Marcel Riesz ( born November 16, 1886 in Győr, Hungary, † September 4, 1969 in Lund, Sweden) was a Hungarian mathematician.
Life
Marcel Riesz was the son of a doctor and the younger brother of Frigyes Riesz. Even as a high school student, he won the Lorand Eötvös contest in 1904. He studied mathematics at the University of Budapest and was influenced by Leopold Fejér. In 1907 he received his doctorate ( summable trigonometric series and power series ). In his thesis he generalized Cantor proof of the uniqueness of the representation of a function by Fourier series of convergent Fourier series on Cesàro - summable. He regularly visited the University of Göttingen and Paris, where he was in 1910/11.
In 1908, he was ( he knew from the International Congress of Mathematicians in Rome 1908) invited for lectures at the University of Stockholm Magnus Gösta Mittag-Leffler. Riesz accepted this invitation and spent the rest of his life in Sweden. In 1926 Riesz an appointment at the University of Lund. 1923 had been there still preferred to him Torsten Carleman, but in 1926 went to Stockholm, where Riesz had at that time also advertised as successor by Helge von Koch in vain. In 1952 he retired, Lund and went to the USA, where he among other things, at the University of Chicago ( where he was 1947/48 Visiting Professor ), the Courant Institute, Stanford University, the University of Washington, Indiana University and University of Maryland was. Due to health problems, he returned in 1960 to Lund back.
His research interests included analytic functions, harmonic analysis, functional analysis, potential theory and wave equations, the set of Kolmogorov - Riesz and Riesz means are connected with his name. In particular, the Riesz means at the time made him internationally known. He theorized related in a Godfrey Harold Hardy book with dar. In the 1930s, he generalized the theory of Liouville -Riemann integral ( see Fractional Calculus, here are named after him Riesz potentials ), which he, inter alia, the Cauchy anwandte problem of the wave equation. In 1949 he published to a great job in the Acta Mathematica .. Later in his career he worked on spinors and Cliffordalgebren.
In 1916 he proved the equivalence of the Riemann hypothesis to a conjecture about the asymptotic behavior of the Riesz function:
Where the denominator is the zeta function at even positions. The Riemann hypothesis is equivalent to
For each (the Landau symbols were used ).
He is ( often named additionally after his students Olof Thorin ( 1912-2004 ), who found a simple proof ) for his theorem on conjugate functions and its convexity theorem known, both released in 1927. Together with his brother Frigyes Riesz, he published only one study in 1916, which contained an important result about the boundary behavior of an analytic function. In 1916, he proved an interpolation trigonometric polynomials with which he gave a new proof of the Bernstein inequality ..
His students include Lars Garding, Einar Hille, Harald Cramér, Otto Frostman (1907-1977, professor at Stockholm University ) and Lars Hörmander.
He was a member of the Royal Swedish Academy of Sciences ( 1936), the Royal Danish Academy of Sciences and the Physio Graphic Society in Lund and an honorary member of the Swedish Mathematical Society. Riesz was honorary doctorates from the universities of Lund and Copenhagen.
Writings
- Collected papers. - Berlin: Springer, 1988 - ISBN 3-540-18115-6.
- Godfrey Harold Hardy with General Theory of Dirichlet Series, Cambridge Tracts, 1915, reprint 1952
- With Emil Hilb Recent Studies on trigonometric series, Encyclopedia of Mathematical Sciences, 1922
- Clifford numbers and spinors, Chapters I to IV, The Institute for Fluid Dynamics and Applied Mathematics, Lecture Series N ° 38, University of Maryland, College Park, Maryland, 1957-1958