theorem). Later, he devised an interpolation theorem to show that the Hilbert transform is a bounded operator in Lp The generalisation of the interpolation theorem by his student Olaf Thorin is now known as the Riesz–Thorin theorem. Riesz also established, independently of Andrey Kolmogorov, what is now called the Kolmogorov–Riesz compactness criterion in Lp: a subset K ⊂Lp(Rn) is precompact if and only if the following three conditions hold: (a) K is bounded; (b) for every there exists so that for every (c) for every there exists so that for every with |y| < ρ, and every . Potential theory, PDE, and Clifford algebras 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. In particular, Riesz discovered the Riesz potential, a generalisation of the Riemann–Liouville integral to dimension higher than one. In the 1940s and 1950s, Riesz worked on Clifford algebras. His 1958 lecture notes, the complete version of which was only published in 1993 (), were dubbed by the physicist David Hestenes "the midwife of the rebirth" of Clifford algebras. Students Riesz's doctoral students in Stockholm include Harald Cramér and Einar Carl Hille. In Lund, Riesz supervised the theses of Otto Frostman, Lars Hörmander, and Olof Thorin. Publications References External links 1886 births 1969 deaths 20th-century Hungarian mathematicians 20th-century Hungarian people 20th-century Swedish people Swedish mathematicians Mathematical analysts Functional analysts Measure theorists People connected to Lund University People from Lund Members of the Royal Swedish Academy of Sciences Emigrants from the Austro-Hungarian Empire to Sweden People from Győr Swedish Jews Austro-Hungarian mathematicians