**Marcel Riesz** was a Hungarian-born mathematician who worked on summation methods, potential theory and other parts of analysis, as well as number theory and partial differential equations.

- Riesz wrote his doctoral thesis Summierbare trigonometrische Reihen und Potenzreihen Ⓣ(Summable trigonometric series and power series) in 1907 and presented it to the University of Budapest; it was published in the following year.
- Von Koch, who was the professor at Stockholm, died in March 1924 and several mathematicians, including Ivar Bendixson and Ivar Fredholm, supported Riesz to fill the vacancy.
- Marcel Riesz's interests ranged from functional analysis to partial differential equations, mathematical physics, number theory and algebra.
- In a joint work with Hardy The general theory of Dirichlet's series, published by Cambridge University Press in 1915, he introduced Riesz means.
- Riesz broadened his range of interests during the 1930 when he became interested in potential theory and in partial differential equations.
- In 1949, Riesz published a 223 page paper L'intégrale de Riemann-Liouville et le problème de Cauchy Ⓣ(The integral of Riemann-Liouville and the Cauchy problem) in which he introduced a multiple integral of Riemann-Liouville type and showed how important this idea is in the theory of the wave equation.
- In Problems related to characteristic surfaces Riesz extended these ideas to obtain the solution of the wave equation for a very general class of characteristic boundaries.
- We noted above that Riesz was interested in number theory but as yet have given no examples of his work in this area.
- Riesz loved to talk about mathematics and he appreciated having listeners.
- Riesz lived alone and these personal lectures took place sometimes in his home, sometimes in his favourite café and sometimes over the telephone.
- Riesz retired in 1952 and went to the United States.
- In 1993 a facsimile reproduction of Riesz's notes from these lectures was published.
- After spending ten years in the United States during which time he continued to work for many hours a day, Riesz suffered a breakdown in 1962 and returned to Lund.
- Among the many honours Riesz received, let us mention his election to the Swedish Academy of Sciences, the Physiographical Society in Lund, and the Videnska Selskab in Copenhagen.

Born 16 November 1886, Györ, Hungary. Died 4 September 1969, Lund, Sweden.

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Origin Hungary

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive