Lamberto Cesari

Lamberto Cesari (23 September 1910 – 12 March 1990) was an Italian mathematician naturalized in the United States, known for his work on the theory of surface area, the theory of functions of bounded variation, the theory of optimal control and on the stability theory of dynamical systems: in particular, by extending the concept of Tonelli plane variation, he succeeded in introducing the class of functions of bounded variation of several variables in its full generality.

Biography In 1933, he was awarded his laurea degree at the Scuola Normale Superiore in Pisa under the direction of Leonida Tonelli. After a period of study from 1934 to 1935 in Germany at Monaco di Baviera under the direction of Constantin Carathéodory, he went back to Pisa at the Scuola Normale Superiore for a year, and then to Rome at the Istituto Nazionale per le Applicazioni del Calcolo, at the time directed by Mauro Picone.

From 1938 to 1946 he went back as a professore incaricato at Pisa University: in 1947 he was at the University of Bologna as a professor of mathematical analysis.

In 1948 he went to the United States as a visiting professor at the Institute for Advanced Study in Princeton, at Purdue University in Lafayette, at the University of California - Berkeley and at the University of Wisconsin–Madison.

In 1960 he was appointed as a professor of mathematical analysis at the University of Michigan at Ann Arbor where he remained until his retirement in 1981. In 1976 he became a citizen of the United States, while keeping close scientific contacts with the Italian mathematical community.

The Lamberto Cesari chair The department of Mathematics at the University of Michigan honoured the memory of Lamberto Cesari with the creation of a professorship chair.

Work

Research activity He is remembered for his achievements on the Plateau's problem, on the theory of parametric minimal surfaces, on Lebesgue measure of continuous and related other variational problems: he also worked in the field of optimal control and studied periodic solutions of systems of nonlinear ordinary differential equations by using methods of nonlinear functional analysis. In the paper he introduced a generalization of functions of bounded variation to the multi-dimensional setting, now acknowledged as the most versatile of such generalizations. He wrote about 250 scientific works on topics such as non linear functional analysis, measure theory, optimal control: his published works include the fundamental monographs , and .

Selected publications

Papers

Scientific papers . Available at Numdam. In this paper, Cesari extends the now called Tonelli plane variation concept in order to include a subclass of the class of integrable functions. .

Biographical, historical and survey papers

. . . "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 their 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).

Books . His work summarizing the theory of surface area, including his own contributions.

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