Giulio Ascoli
Encyclopedia
Giulio Ascoli was an 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 Politecnico di Milano University. From 1879 he was professor of mathematics at the Reale Istituto Tecnico Superiore, where, in 1901, was affixed a plaque that remembers him.
He was also corresponding member of Istituto Lombardo.
He made contributions to the theory of functions of a real variable and to Fourier series
. For example, Ascoli introduced equicontinuity
in 1884, a topic regarded as one of the fundamental concepts in the theory of real functions. In 1889, Italian mathematician Cesare Arzelà
generalized Ascoli's Theorem into the Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.
). Available from the website of the Società Italiana di Storia delle Matematiche.
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. He was a student of the Scuola Normale di Pisa
Scuola Normale Superiore di Pisa
The Scuola Normale Superiore di Pisa, also known in Italian as Scuola Normale , is a public higher learning institution in Italy. It was founded in 1810, by Napoleonic decree, as a branch of the École Normale Supérieure of Paris...
, where he graduated in 1868.
In 1872 he became Professor of Algebra and Calculus of the Politecnico di Milano University. From 1879 he was professor of mathematics at the Reale Istituto Tecnico Superiore, where, in 1901, was affixed a plaque that remembers him.
He was also corresponding member of Istituto Lombardo.
He made contributions to the theory of functions of a real variable and to Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
. For example, Ascoli introduced equicontinuity
Equicontinuity
In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein...
in 1884, a topic regarded as one of the fundamental concepts in the theory of real functions. In 1889, Italian mathematician Cesare Arzelà
Cesare Arzelà
Cesare Arzelà was an Italian mathematician who taught at the University of Bologna and is recognized for his contributions in the theory of functions, particularly for his characterization of sequences of continuous functions, generalizing the one given earlier by Giulio Ascoli in the famous...
generalized Ascoli's Theorem into the Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.
Further reading
(in ItalianItalian language
Italian 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...
). Available from the website of the Società Italiana di Storia delle Matematiche.
External links
- Biography in Italian.
- Ascoli, Julio in the Jewish EncyclopediaJewish EncyclopediaThe Jewish Encyclopedia is an encyclopedia originally published in New York between 1901 and 1906 by Funk and Wagnalls. It contained over 15,000 articles in 12 volumes on the history and then-current state of Judaism and the Jews as of 1901...
. - By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematics by T. Koetsier, J. Van Mill, an article containing a history of Ascoli's work on the Arzelà-Ascoli theoremArzelà-Ascoli theoremIn mathematics, the Arzelà–Ascoli theorem of functional analysis gives necessary and sufficient conditions to decide whether every subsequence of a given sequence of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence. The main condition...
.