Giulio Ascoli
{{Short description|Jewish-Italian mathematician (1843–1896)}}
{{distinguish|Guido Ascoli}}
{{Infobox scientist
|name = Giulio Ascoli
|box_width =
|caption =
|birth_date = {{Birth date|df=yes|1843|1|20}}
|death_date = {{Death date and age|df=yes|1896|7|12|1843|1|20}}
|birth_place = Trieste, Austrian Empire
|death_place = Milan, Italy
|nationality = Italian
|field = Mathematics
|known_for =
|notable_students =
|prizes =
}}
Giulio Ascoli (20 January 1843, Trieste, Austrian Empire – 12 July 1896, Milan) was a Jewish-Italian{{JewishEncyclopedia|url=http://www.jewishencyclopedia.com/articles/1900-ascoli-giulio|article=Ascoli, Giulio}} 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 a 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.According to {{Harvtxt|Dshalalow|2001|p=153}}. In 1889, Italian mathematician Cesare Arzelà generalized Ascoli's Theorem into the Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.See {{Harvtxt|Dshalalow|2001|p=153}}.
See also
Notes
{{Reflist|29em}}
Biographical references
- {{Citation
| last1 = Guerraggio
| first1 = Angelo
| author-link = Angelo Guerraggio
| last2 = Nastasi
| first2 = Pietro
| author2-link = Pietro Nastasi
| title = Italian mathematics between the two world wars
| place = Basel
| publisher = Birkhäuser Verlag
| year = 2005
| series = Science Networks. Historical Studies
| volume = 29
| pages = x+299
| url = https://books.google.com/books?id=fl0gL50heXcC
| doi = 10.1007/3-7643-7512-4
| mr = 2188015
| zbl = 1084.01010
| isbn = 3-7643-6555-2
}}.
- {{cite book
| first = G. F.
| last = Tricomi
| author-link = Francesco Tricomi
| contribution = Giulio Ascoli
| contribution-url = http://www.dm.unito.it/sism/m_italiani/biografie/tricomi/ascoligiu.html
| title = Matematici italiani del primo secolo dello stato unitario (Italian mathematicians of the first century of the unitary state)
| series = Memorie dell'Accademia delle Scienze di Torino. Classe di Scienze fisiche matematiche e naturali, series IV
| volume = I
| year = 1962
| pages = 120
| zbl = 0132.24405
| access-date = 31 July 2010
| archive-date = 28 July 2012
| archive-url = https://web.archive.org/web/20120728210157/http://www.dm.unito.it/sism/m_italiani/biografie/tricomi/ascoligiu.html
| url-status = bot: unknown
}}(in Italian). Available from the website of the.
References
- {{citation
|title= Real analysis: an introduction to the theory of real functions and integration
|last= Dshalalow
|first= Jewgeni H.
|year= 2001
|series= Studies in Advanced Mathematics
|publisher= CRC Press
|location= Boca Raton, Florida
|pages=xiv+567
|isbn= 1-58488-073-2
|url=https://books.google.com/books?id=9S09YpoodHIC&pg=PA153
|mr=1788725
|zbl=0978.28001
}}.
- {{Citation
|last = Letta
|first = Giorgio
|author-link = Giorgio Letta
|title = Le condizioni di Riemann per l'integrabilità e il loro influsso sulla nascita del concetto di misura
|volume = XVIII
|issue = 1
|pages = 143–169
|orig-year = 112°
|year = 1994
|language = Italian
|url = http://media.accademiaxl.it/memorie/Serie5_V18_P1.pdf
|mr = 1327463
|zbl = 0852.28001
|url-status = dead
|archive-url = https://web.archive.org/web/20140228144250/http://media.accademiaxl.it/memorie/Serie5_V18_P1.pdf
|archive-date = 2014-02-28
}}. "Riemann's conditions for integrability and their influence on the birth of the concept of measure" (English translation of title) is an article on the history of measure theory, analyzing deeply and comprehensively every early contribution to the field, starting from Riemann's work and going to the works of Hermann Hankel, Gaston Darboux, Giulio Ascoli, Henry John Stephen Smith, Ulisse Dini, Vito Volterra, Paul David Gustav du Bois-Reymond and Carl Gustav Axel Harnack.
External links
- [https://web.archive.org/web/20050329000140/http://matematica.uni-bocconi.it/storia/letteraa/biogr-ascoli.htm Biography] in Italian.
- [http://www.jewishencyclopedia.com/view.jsp?artid=1900&letter=A&search=ascoli Ascoli, Julio] in the Jewish Encyclopedia.
- [http://www.cs.vu.nl/~vanmill/papers/papers1999/teun.pdf 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 theorem.
{{Authority control}}
{{Use dmy dates|date=March 2018}}
{{DEFAULTSORT:Ascoli, Giulio}}
Category:19th-century Italian mathematicians
Category:Mathematical analysts
Category:Academic staff of the Polytechnic University of Milan
Category:19th-century Italian Jews
{{Italy-mathematician-stub}}