Марсель Рис: венгр математигі және оның ғылыми еңбектері

Hungarian mathematician

Marcel Riesz (Riesz Marcell ; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras. He spent most of his career in Lund, Sweden. Marcel is the younger brother of Frigyes Riesz, who was also an important mathematician and at times they worked together (see F. and M. Riesz theorem).

Marcel Riesz was born in Győr, Austria Hungary. He was the younger brother of the mathematician Frigyes Riesz. In 1904, he won the Loránd Eötvös competition. Riesz was elected a member of the Royal Swedish Academy of Sciences in 1936. His results on summability of trigonometric series include a generalisation of Fejér's theorem to Cesàro means of arbitrary order. He also studied the summability of power and Dirichlet series, and coauthored a book on the latter with G. H. Hardy. He also introduced the Riesz function Riesz(x), and showed that the Riemann hypothesis is equivalent to the bound as x → ∞, for any ε > 0. Together with his brother Frigyes Riesz, he proved the F. and M. Riesz theorem, which implies, in particular, that if μ is a complex measure on the unit circle such that

then the variation |μ| of μ and the Lebesgue measure on the circle are mutually absolutely continuous.

After 1930, the interests of Riesz shifted to potential theory and partial differential equations. He made use of "generalised potentials", generalisations of the Riemann–Liouville integral.

Riesz's doctoral students in Stockholm include Harald Cramér and Einar Carl Hille. In Lund, Riesz supervised the theses of Otto Frostman, Lars Gårding, Lars Hörmander, and Olof Thorin.