Leonida Tonelli
Italian mathematician (1885–1946)
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Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, noted for proving Tonelli's theorem, a variation of Fubini's theorem, and for introducing semicontinuity methods as a common tool for the direct method in the calculus of variations.[1]
Leonida Tonelli | |
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| Born | 19 April 1885 Gallipoli, Apulia, Italy |
| Died | 12 March 1946 (aged 60) Pisa, Italy |
| Alma mater | University of Bologna |
| Known for | Tonelli's theorem Tonelli's theorem (functional analysis) Tonelli–Hobson test |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Cagliari University of Parma University of Bologna University of Pisa Scuola Normale Superiore |
| Doctoral advisor | Cesare Arzelà |
| Doctoral students | Emilio Baiada Paolo Budinich Lamberto Cesari Guido Stampacchia |
Education
Tonelli graduated from the University of Bologna in 1907; his Ph.D. thesis was written under the direction of Cesare Arzelà.[2]
Work
He is one of the founders of Modern Theory of Functions of Real Variables and his work on the Calculus of Variations is a milestone in analysis.[3]
— Olga Arsenievna Oleinik, (Oleinik 1986, p. 28)
The present writer's father, W. H. Young, used to recall that this very question — what principle can we use as the foundation of the calculus of variations[4] — had been put him by a young Italian mathematician. His reply was a question: "Can you use semicontinuity?" The young Italian was Leonida Tonelli. Semicontinuity was then still a recent concept, known only to a few. In the hands of Tonelli, it became an important tool in a fundamental new approach to the calculus of variations.
— Laurence Chisholm Young, (Young 1969, p. 153)
Selected publications
- Opere scelte, a cura dell'Unione matematica italiana e col contributo del Consiglio nazionale delle ricerche, 1900
- Fondamenti di Calcolo delle Variazioni. Zanichelli, Bologna, vol. 1: 1922,[5] vol. 2: 1923
- Tonelli, Leonida (1925). "The Calculus of Variations". Bulletin of the American Mathematical Society. 31 (3–4): 163–172. doi:10.1090/s0002-9904-1925-04002-1. MR 1561014.
- Serie trigonometriche. Zanichelli, Bologna 1928[6]
