Leonida Tonelli

Leonida Tonelli
Born	19 April 1885 Gallipoli, Apulia, Italy
Died	12 March 1946 (aged 60) Pisa, Italy
Nationality	Italian
Fields	Mathematics
Institutions	University of Cagliari University of Parma University of Bologna University of Pisa Scuola Normale Superiore
Alma mater	University of Bologna
Doctoral advisor	Cesare Arzelà
Doctoral students	Lamberto Cesari, Guido Stampacchia
Known for	Tonelli's theorem

Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, noted for creating 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]

Education

Tonelli graduated from the University of Bologna in 1907.

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.^[2]

— 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^[3] — 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 richerche, 1900
• Fondamenti di Calcolo delle Variazioni. Zanichelli, Bologna, vol. 1: 1922,^[4] vol. 2: 1923
• "The Calculus of Variations". Bull. Amer. Math. Soc. 31: 163–172. 1925. doi:10.1090/s0002-9904-1925-04002-1. MR 1561014.
• Serie trigonometriche. Zanichelli, Bologna 1928^[5]

See also

• Calculus of variations
• Fourier series
• Lebesgue integral
• Mathematical analysis

Notes

1. Leonida Tonelli.
2. The quote is reported verbatim, including the uppercase emphasis on the mathematical topics cited.
3. As also recalled by Sneddon (1986, p. 36).
4. Dresden, Arnold (1926). "Review: Fondamenti di Calcolo delle Variazioni, Vol. 1, by Leonida Tonelli" (PDF). Bull. Amer. Math. Soc. 32 (4): 381–386. doi:10.1090/s0002-9904-1926-04231-2.
5. Tamarkin, J. D. (1929). "Review: Serie trigonometriche by Leonida Tonelli" (PDF). Bull. Amer. Math. Soc. 35 (6): 871–874. doi:10.1090/s0002-9904-1929-04813-4.

References

Biographical and general references

• Cesari, Lamberto (1946), "Leonida Tonelli (1885-1946)", Bollettino dell'Unione Matematica Italiana, Serie 3 (in Italian) 1 (1): 64–67, available from the Biblioteca Digitale Italiana di Matematica.
• Cesari, Lamberto (1986), "L'opera di Leonida Tonelli e la sua influenza nel pensiero scientifico del secolo", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei (in Italian) 77, Roma: Accademia Nazionale dei Lincei, pp. 41–73. "The work of Leonida Tonelli and his influence on scientific thinking in this century" (English translation of the title) is an ample commemorative article, reporting recollections of the Author about teachers and colleagues, and a detailed survey of his and theirs scientific work, presented at the International congress in occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985).
• Cinquini, Silvio (1950), "Leonida Tonelli", Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Serie II (in Italian) 15 (1–4): 1–37, MR MR1556828, Zbl 0036.00505.
• Faedo, Sandro (1986), "Leonida Tonelli e la scuola matematica pisana", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei (in Italian) 77, Roma: Accademia Nazionale dei Lincei, pp. 89–109. "Leonida Tonelli and the Pisa mathematical school" is a survey of the work of Tonelli in Pisa and his influence on the development of the school, presented at the International congress in occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985). The Author was one of his pupils and, after his death, held his chair of mathematical analysis at the University of Pisa, becoming dean of the faculty of sciences and then rector: he exerted a strong positive influence on the development of the university.
• Fichera, Gaetano (1995), "Tre battaglie perdute da tre grandi matematici italiani", Atti del convegno di studi in memoria di Giuseppe Gemignani. Modena, 20 maggio 1994, Collana di Studi dell'Accademia (in Italian) 11, Modena: Enrico Mucchi Editore on behalf of the Accademia Nazionale di Scienze, Lettere e Arti di Modena, pp. 9–28, MR 1385469 External link in |publisher= (help). This paper, included in the Proceedings of the Study Meeting in Memory of Giuseppe Gemignani, is an account of the failures of Vito Volterra, Leonida Tonelli and Francesco Severi, when dealing with particular research problems during their career. An English translation of the title reads as:-"Three battles lost by three great Italian mathematicians".
• Oleinik, O. A. (1986), "Indirizzo di adesione", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei 77, Roma: Accademia Nazionale dei Lincei, p. 26. The brief "participating address" presented to the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985) by Olga Oleinik on behalf of the Moscow Mathematical Society.
• Rizza, Giovanni Battista (1986), "Indirizzo di adesione", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei 77, Roma: Accademia Nazionale dei Lincei, pp. 29–30. The brief "participating address" presented to the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985), by Giovanni Battista Rizza on behalf of the University of Parma: the scientific relations between Leonida Tonelli and the Department of Mathematics in Parma are described.
• Sansone, Giovanni (1946), "Leonida Tonelli", Annali di Matematica Pura ed Applicata, IV Serie (in Italian) XXV: XIII–XVI, doi:10.1007/BF02418076, Zbl 0061.00604. The commemoration of Tullio Levi Civita, Guido Fubini, Leonida Tonelli and Michele De Franchis published on the "Annali di Matematica". Note that the paper is not signed: the Author is disclosed by Cinquini (1950, p.1, footnote (1)).
• Sneddon, Ian (1986), "Indirizzo di adesione", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei 77, Roma: Accademia Nazionale dei Lincei, pp. 35–36. Some recollections about Mauro Picone and Leonida Tonelli, presented by Ian Sneddon as the "participating address" (Italian translation of the title of the contribution) to the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985) on behalf of the Royal Society of London and of the Royal Society of Edinburgh.

Scientific references

• Cafiero, Federico (1959), Misura e integrazione, Monografie matematiche del Consiglio Nazionale delle Ricerche (in Italian) 5, Roma: Edizioni Cremonese, pp. VII+451, MR 0215954, Zbl 0171.01503. Measure and integration (as the English translation of the title reads) is a definitive monograph on integration and measure theory: the treatment of the limiting behavior of the integral of various kind of sequences of measure-related structures (measurable functions, measurable sets, measures and their combinations) is somewhat conclusive.
• Giusti, Enrico (1994), Metodi diretti nel calcolo delle variazioni, Monografie Matematiche (in Italian), Bologna: Unione Matematica Italiana, pp. VI+422, MR 1707291, Zbl 0942.49002, translated in English as Giusti, Enrico (2003), Direct Methods in the Calculus of Variations, River Edge, NJ – London – Singapore: World Scientific Publishing, pp. viii+403, ISBN 981-238-043-4, MR 1962933, Zbl 1028.49001.
• Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., eds. (1986), Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei 77, Roma: Accademia Nazionale dei Lincei, p. 318. The proceedings of the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli, held in Rome on May 6–9, 1985, at the Accademia Nazionale dei Lincei.
• Young, L. C. (1969), Lectures on the Calculus of Variation and Optimal Control, Philadelphia–London–Toronto: W. B. Saunders, pp. xi+331, MR 0259704, Zbl 0177.37801.

External links

O'Connor, John J.; Robertson, Edmund F., "Leonida Tonelli", MacTutor History of Mathematics archive, University of St Andrews.