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| Riesz brothers | |
|---|---|
| Name | Riesz brothers |
| Nationality | Hungarian |
| Fields | Mathematics |
| Institutions | University of Szeged, University of Budapest, École Normale Supérieure, University of Paris, Institute for Advanced Study, Royal Swedish Academy of Sciences |
| Alma mater | Eötvös Loránd University, University of Budapest |
| Known for | Riesz representation theorem, Riesz transform, Riesz potential, Riesz–Markov–Kakutani representation theorem |
Riesz brothers were two Hungarian mathematicians, Frigyes Riesz and Marcel Riesz, who made foundational contributions to functional analysis, harmonic analysis, and operator theory during the early to mid-20th century. Their work intersects with major figures and institutions such as David Hilbert, John von Neumann, Stefan Banach, Norbert Wiener, and Maurice Fréchet, and influenced developments at centers including University of Szeged, University of Paris, Institute for Advanced Study, and Royal Swedish Academy of Sciences. The brothers' theorems and methods shaped subsequent research by mathematicians like Marcel Riesz's students and contemporaries including Lars Ahlfors, Salomon Bochner, and Håkan Hedenmalm.
Frigyes Riesz was born in Békéscsaba and Marcel Riesz in Szeged; both studied at Eötvös Loránd University and the University of Budapest under influences from mentors associated with Miklós Schweitzer and contemporaries linked to Gyula Kőnig. Frigyes held positions at University of Szeged and later at University of Budapest and spent time interacting with scholars at École Normale Supérieure and University of Paris, while Marcel held appointments that connected him with Swedish institutions and collaborations across Stockholm and Gothenburg. Their careers overlapped with major mathematical movements including the rise of functional analysis in Germany and Poland, and exchanges with figures from Princeton University and Institute for Advanced Study. Both navigated the intellectual currents around events such as the World War I and World War II, corresponding with mathematicians like Felix Hausdorff, Stefan Banach, Hermann Weyl, Émile Borel, and Tullio Levi-Civita.
The brothers made complementary contributions: Frigyes developed abstract foundations in Hilbert space theory and linear operators that connected to results by David Hilbert and Erhard Schmidt, while Marcel focused on concrete estimates in harmonic analysis, singular integrals, and boundary value problems akin to work by Antoni Zygmund and Norbert Wiener. Their papers touched on subjects central to Banach space theory, spectral theory related to John von Neumann, and measure representations paralleling the Riesz–Markov–Kakutani representation theorem which interacts with ideas from Andrey Kolmogorov and Paul Lévy. Techniques introduced or popularized by them influenced research on Fourier series problems that concerned G. H. Hardy, J. E. Littlewood, and Salem, and operator inequalities used by Marshall Stone and Issai Schur.
Key results attributed to the brothers include the Riesz representation theorem in Hilbert space contexts, Riesz transforms in Euclidean space harmonic analysis, and Riesz potentials linked to fractional integration related to Sobolev spaces and Sobolev-type embeddings studied by Sergei Sobolev. The Riesz–Markov–Kakutani representation theorem established correspondence between linear functionals and measures akin to work by Andrei Kolmogorov in probability theory. Their theorems provided tools for spectral analysis of unbounded operators in settings developed further by T. Kato and Kurt Friedrichs, and underpinned interpolation theory pursued by Lars Hörmander and B. Sz.-Nagy. Consequences of their work appear in modern treatments by Elias Stein, Charles Fefferman, Terence Tao, and Jean Bourgain.
The Riesz brothers shaped curricula and research programs at institutions such as University of Szeged, University of Budapest, and influenced schools in France, Poland, Sweden, and United States. Their ideas permeate textbooks by Marshall Stone, John Conway, Elias Stein, and Walter Rudin, and underpin methods used in problems originating with Laurent Schwartz and Israel Gelfand. Applications of their work extend to modern research areas pursued by mathematicians at institutions like Princeton University, Massachusetts Institute of Technology, University of Cambridge, and University of California, Berkeley, and contribute to contemporary studies by figures such as Terence Tao, Cédric Villani, Andrew Wiles, and Peter Sarnak. Theorems bearing their names continue to appear in seminars and conferences organized by International Mathematical Union, European Mathematical Society, and national academies including Royal Swedish Academy of Sciences and Hungarian Academy of Sciences.
- Papers by Frigyes appeared in journals associated with Mathematical Reviews and venues frequented by Felix Hausdorff and André Weil; Marcel's papers appeared alongside work by Antoni Zygmund and Norbert Wiener. Key monographs and articles were influential for researchers such as Elias Stein, Charles Fefferman, Lars Hörmander, and Jean-Pierre Kahane. Their collected works influenced expositions by Israel Gelfand, Alain Connes, A. Grothendieck, and Jean Dieudonné.
The brothers received recognition from institutions including the Hungarian Academy of Sciences and interactions with awards and societies such as Royal Swedish Academy of Sciences events and conferences sponsored by the International Mathematical Union and European Mathematical Society. Their legacy is commemorated in lecture series and memorial volumes alongside honored mathematicians like Felix Hausdorff, Stefan Banach, John von Neumann, David Hilbert, and André Weil.
Category:Hungarian mathematicians Category:Functional analysts Category:Harmonic analysts