Lamberto Cesari
Encyclopedia
Lamberto Cesari was an Italian
mathematician
naturalized in the United States
.
at the Scuola Normale Superiore at 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 department of Mathematics at the University of Michigan
honored the memory of Lamberto Cesari with the creation of a professorship chair, currently held by the mathematician Joel Smoller.
, on the theory of parametric minimal surface
s, 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 equation
s 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 generaizations. He wrote about 250 scientific works on topics such as non linear functional analysis
, measure theory, optimal control
: his published works include the fundamental monograph
s , and .
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
naturalized in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
.
Biography
In 1933, he was awarded his laureaLaurea
In Italy, the laurea is the main post-secondary academic degree.-Reforms due to the Bologna process:Spurred by the Bologna process, a major reform was instituted in 1999 to introduce easier university degrees comparable to the bachelors...
at the Scuola Normale Superiore at Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...
under the direction of Leonida Tonelli
Leonida Tonelli
Leonida Tonelli was an Italian mathematician, most noted for creating Tonelli's theorem, usually considered a forerunner to Fubini's theorem.-External links:...
. After a period of study from 1934 to 1935 in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
at Monaco di Baviera under the direction of Constantin Carathéodory
Constantin Carathéodory
Constantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...
, he went back to Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...
at the Scuola Normale Superiore for a year, and then to Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
at the Istituto Nazionale per le Applicazioni del Calcolo, at the time directed by Mauro Picone
Mauro Picone
Mauro Picone was an Italian mathematician. He is known for the Picone identity, for the Sturm-Picone comparison theorem and for being the founder of the Istituto Nazionale per le Applicazioni del Calcolo, presently named after him...
. From 1938 to 1946 he went back as a professore incaricato at Pisa University: in 1947 he was at the University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
as a professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. In 1948 he went to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
as a visiting professor at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, at Purdue University
Purdue University
Purdue University, located in West Lafayette, Indiana, U.S., is the flagship university of the six-campus Purdue University system. Purdue was founded on May 6, 1869, as a land-grant university when the Indiana General Assembly, taking advantage of the Morrill Act, accepted a donation of land and...
in Lafayette
Lafayette, Indiana
Lafayette is a city in and the county seat of Tippecanoe County, Indiana, United States, northwest of Indianapolis. As of the 2010 census, the city had a total population of 67,140. West Lafayette, on the other side of the Wabash River, is home to Purdue University, which has a large impact on...
, at the University of California - Berkeley and at the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
. In 1960 he was appointed as a professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of 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
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, while keeping close scientific contacts with the Italian mathematical community.
The department of Mathematics at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
honored the memory of Lamberto Cesari with the creation of a professorship chair, currently held by the mathematician Joel Smoller.
Research activity
He is remembered for his achievements on the Plateau's problemPlateau's problem
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who was interested in soap films. The problem is considered part of the calculus of variations...
, on the theory of parametric minimal surface
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....
s, on Lebesgue measure
Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space. For n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called...
of continuous
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
and related other variational problems: he also worked in the field of optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
and studied periodic solutions of systems of nonlinear ordinary differential equation
Ordinary differential equation
In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s by using methods of nonlinear functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. In the paper he introduced a generalization of functions of bounded variation
Bounded variation
In mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded : the graph of a function having this property is well behaved in a precise sense...
to the multi-dimensional setting, now acknowledged as the most versatile of such generaizations. He wrote about 250 scientific works on topics such as non linear functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, measure theory, optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
: his published works include the fundamental monograph
Monograph
A monograph is a work of writing upon a single subject, usually by a single author.It is often a scholarly essay or learned treatise, and may be released in the manner of a book or journal article. It is by definition a single document that forms a complete text in itself...
s , and .
See also
- Bounded variationBounded variationIn mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded : the graph of a function having this property is well behaved in a precise sense...
- Constantin CarathéodoryConstantin CarathéodoryConstantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...
- Mauro PiconeMauro PiconeMauro Picone was an Italian mathematician. He is known for the Picone identity, for the Sturm-Picone comparison theorem and for being the founder of the Istituto Nazionale per le Applicazioni del Calcolo, presently named after him...
- Leonida TonelliLeonida TonelliLeonida Tonelli was an Italian mathematician, most noted for creating Tonelli's theorem, usually considered a forerunner to Fubini's theorem.-External links:...
- Total variationTotal variationIn mathematics, the total variation identifies several slightly different concepts, related to the structure of the codomain of a function or a measure...
External links
- PRISTEM bibliography (in ItalianItalian languageItalian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
). - The Centro Studi Interfacoltà Lamberto Cesari at the University of PerugiaUniversity of PerugiaUniversity of Perugia is a public-owned university based in Perugia, Italy. It was founded in 1308, as attested by the Bull issued by Pope Clement V certifying the birth of the Studium Generale....
, and a biography of Lamberto Cesari (in ItalianItalian languageItalian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
).