Marcel Riesz (26 September 1900 – 15 March 1993) was a Hungarian‑born mathematician who made significant contributions to real and complex analysis, functional analysis, and harmonic analysis. He was the younger brother of Frigyes Riesz, another prominent mathematician.
Early life and education
Marcel Riesz was born in Budapest, then part of Austria‑Hungary, into a family of Jewish descent. He studied at the University of Budapest, where he earned his Ph.D. in 1922 under the supervision of Lipót Fejér. His doctoral dissertation concerned Fourier series and introduced techniques that would later be central to his research.
Academic career
After completing his doctorate, Riesz held positions at several European universities, including the University of Leipzig and the University of Lund. In 1930, he accepted a professorship at the University of Lund in Sweden, where he remained for the majority of his career. In 1956, he moved to the United States to become a professor at the University of California, Los Angeles (UCLA), where he worked until his retirement in 1970.
Research contributions
Riesz’s work spans multiple areas of analysis:
- Riesz interpolation theorem – Developed with his brother Frigyes, this theorem provides a method for interpolating linear operators between Lebesgue spaces, forming a foundational tool in functional analysis.
- Riesz–Thorin theorem – A generalization of the interpolation theorem, independently discovered by Riesz and G. Olof Thorin, which gives bounds for linear operators acting between $L^p$ spaces.
- Riesz convexity theorem – An earlier result concerning the convexity properties of norms of linear operators.
- Riesz potentials – Introduced a class of integral operators now known as Riesz potentials, which are essential in potential theory and fractional integration.
- Harmonic analysis – Made contributions to the theory of singular integrals, Fourier transforms, and the study of spherical means.
Publications and influence
Riesz authored numerous research articles and several influential textbooks, including "Fourier Series" and "Classical Harmonic Analysis" (co‑authored with Elias M. Stein). His work has had lasting impact on modern analysis, and many concepts bearing his name continue to be central in contemporary mathematical research.
Honors and awards
- Member of the Royal Swedish Academy of Sciences (elected 1945).
- Honorary doctorate from the University of Lund (1961).
- Recognized as a Fellow of the American Mathematical Society (posthumously honored in 2012 for his contributions).
Personal life and death
Marcel Riesz married in 1932 and had two children. He became a naturalized Swedish citizen in 1940 and later obtained U.S. citizenship after moving to California. Riesz passed away in Los Angeles, California, at the age of 92.
Legacy
Riesz’s theorems and methods are integral to functional analysis, partial differential equations, and mathematical physics. The “Riesz” name appears in numerous concepts—such as Riesz transforms, Riesz potentials, and Riesz spaces—reflecting the breadth of his contributions to mathematics.