Lamberto Cesari

Lamberto Cesari (born September 23, 1910 in Bologna , † March 12, 1990 in Ann Arbor ) was an Italian-American mathematician who dealt with analysis and especially differential equations , functional analysis and the calculus of variations .

life and work

Cesari studied at the Scuola Normale Superiore in Pisa with the Laurea degree in 1933 with Leonida Tonelli ( Sulle condizioni sufficienti per le successioni di Fourier ). After that he was at the Ludwig Maximilians University in Munich with Constantin Caratheodory , in 1935 again for a year in Pisa and then in Rome at the Istituto Nazionale per le Applicazioni del Calcolo with Mauro Picone . In 1938 he became an assistant professor (Professore incaricato) at the University of Pisa .

From 1942 he was a professor at the University of Bologna , where he received the chair of mathematical physics in 1947 after a competition that was common in Italy. In 1948 he went to the USA as a visiting professor at the Institute for Advanced Study . He was at Purdue University , 1949 at the University of California, Berkeley , and 1950 at the University of Wisconsin – Madison . In 1960 he became professor of mathematical analysis at the University of Michigan at Ann Arbor . From 1976 he was RL Wilder Distinguished Professor . In 1980 he retired there.

Among other things, he dealt with areas and minimal areas (e.g. plateau problem ), optimal control theory, periodic solutions of nonlinear common differential equation systems with the methods of nonlinear functional analysis and with measure theory. In 1936 he generalized functions of limited variation to several dimensions. With the Lebesgue integrable functions of limited variation, later called BVC functions, he proved, among other things, in 1937 that the generalized surface integral of (where f can have discontinuities) is finite if and only if a BVC function is (which is Tonelli's theorem for the case more continuous) Generalized functions) and he proved that the double Fourier series of a BVC function converges to f almost everywhere. Also in 1937 he published an influential paper on iterative solution methods for systems of differential equations. In the early 1940s he gave necessary and sufficient conditions for the finiteness of the Lebesgue area of ​​an area given by a parametric equation. ${\displaystyle z=f(x,y)}$ ${\displaystyle f(x,y)}$ ${\displaystyle z=f(x,y)}$

He has published over 250 scientific papers and three monographs.

A chair is named after him at the University of Michigan. Jack K. Hale is one of his PhD students .

Cesari was invited speaker at the International Congress of Mathematicians in Cambridge in 1960 ( Applications of area theory in analysis , with Tibor Radó ) and in Amsterdam in 1954 ( Retraction, Homotopy, Integral ).

He was a member of the Accademia dei Lincei and the Academies of Science in Bologna, Modena and Milan. In 1976 he received an honorary doctorate from the University of Perugia .

He became a US citizen in 1976. He was married to the German Isotta Hornauer, whom he knew from his student days in Munich. She worked as a translator of mathematical works and published with Lamberto Cesari on the history of mathematics (Mathematics in the Mediterranean: Today's view, University of Perugia 1990, on the occasion of Cesari's honorary doctorate in Perugia).

Fonts

• Surface Area, Annals of Mathematical Studies 35, Princeton University Press 1956
• Asymptotic behavior and stability problems for ordinary differential equations, Results of Mathematics and their Frontier Areas, Springer Verlag, 1959, 1962, 1971
• Optimization Theory and Applications. Problems with ordinary differential equations, Applications of Mathematics 17, Springer Verlag 1983
• Sulle funzioni a variazione limitata, Annali della Scuola Normale Superiore, Series II, Volume 5 1936, pp. 299-313
• Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive, Atti Accad. Naz. Lincei, Phys.-Math. Class, 1937, pp. 422-428

literature

• J. Cecconi, Lamberto Cesari, Boll. U.N. Mat. Ital. A, Vol. 6, 1992, pp. 125-151.
• JK Hale: In memoriam: Lamberto Cesari (1910-1990), J. Differential Equations, Volume 96, 1992, pp. 201-202.
• Lamberto Cesari: 1910–1990, Notices Amer. Math. Soc., Vol. 37, 1990, p. 677.
• D. Graffi: On the contributions of Lamberto Cesari to applied mathematics, in: Nonlinear analysis and optimization, Bologna, 1982, Lecture Notes in Mathematics 1107, Springer Verlag 1984, pp. 1-18.

Web links

• John J. O'Connor, Edmund F. Robertson :  Lamberto Cesari. In: MacTutor History of Mathematics archive .

Individual evidence

1. ^ Mathematics Genealogy Project
2. ^ In 1957 she published a poem about mathematicians in the American Mathematical Monthly, Volume 64, p. 420, Residues of Ideals