Cesare Arzelà (6 March 1847 – 15 March 1912) was an Italian
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who taught at the
University of Bologna
The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
and is recognized for his contributions in the
theory of functions, particularly for his characterization of
sequences
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called t ...
of
continuous function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value ...
s, generalizing the one given earlier by
Giulio Ascoli
Giulio Ascoli (20 January 1843, Trieste – 12 July 1896, Milan) was a Jewish-Italian mathematician. He was a student of the Scuola Normale di Pisa, where he graduated in 1868.
In 1872 he became Professor of Algebra and Calculus of the Politecn ...
in the
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded inter ...
.
Life
He was a pupil of the
Scuola Normale Superiore
The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students.
It was founded in 1810 wi ...
of
Pisa
Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the cit ...
where he graduated in 1869. Arzelà came from a poor household; therefore he could not start his study until 1871, when he studied in Pisa under
Enrico Betti
Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations, giv ...
and
Ulisse Dini
Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian mathematician and politician, born in Pisa. He is known for his contribution to real analysis, partly collected in his book "''Fondamenti per la teorica delle funzioni di variabili ...
.
He was working in
Florence
Florence ( ; it, Firenze ) is a city in Central Italy and the capital city of the Tuscany region. It is the most populated city in Tuscany, with 383,083 inhabitants in 2016, and over 1,520,000 in its metropolitan area.Bilancio demografico an ...
(from 1875) and in 1878 obtained the Chair of Algebra at the
University of Palermo
The University of Palermo ( it, Università degli Studi di Palermo) is a university located in Palermo, Italy, and founded in 1806. It is organized in 12 Faculties.
History
The University of Palermo was officially founded in 1806, although its ...
.
After that he became a professor in 1880 at the
University of Bologna
The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
at the department of analysis. He conducted research in the field of
theory of functions. His most famous student was
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 calc ...
.
In 1889 he generalized the
Ascoli Ascoli may refer to:
Places in Italy
*Ascoli Satriano, a town and ''comune'' in the province of Foggia in the Apulia region
*Province of Ascoli Piceno, a province of the Marche region
** Ascoli Piceno, a city which is the seat of the province above ...
theorem to
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded inter ...
, an important
theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...
in the theory of functions.
He was a member of the
Accademia Nazionale dei Lincei
The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rom ...
, and of several other academies.
Works
*
See also
*
Total variation
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure. For a real-valued continuous function ''f'', defined on an interval 'a'' ...
Further reading
*. Available from the website of the
External links
*
1847 births
1912 deaths
20th-century Italian mathematicians
Mathematical analysts
University of Palermo faculty
{{Italy-mathematician-stub