Leonida Tonelli

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]

Leonida Tonelli
Born(1885-04-19)19 April 1885
Died12 March 1946(1946-03-12) (aged 60)
Pisa, Italy
NationalityItalian
Alma materUniversity of Bologna
Known forTonelli's theorem
Scientific career
FieldsMathematics
InstitutionsUniversity of Cagliari
University of Parma
University of Bologna
University of Pisa
Scuola Normale Superiore
Doctoral advisorCesare Arzelà
Doctoral studentsEmilio 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]

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.

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,[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]

See also

Notes

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

References

Biographical and general references

Scientific references

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