Eugenio Elia Levi Explained

Eugenio Elia Levi
Birth Date:	1883 10, df=yes
Birth Place:	Torino, Italy
Death Place:	Cormons, Italy
Nationality:	Italian
Fields:	Group theory Several complex variables Partial differential operators
Workplaces:	Scuola Normale Superiore University of Genoa
Alma Mater:	Scuola Normale Superiore
Known For:	Levi decomposition Levi form Parametrix Pseudoconvexity
Awards:	Lavagna prize (1904) Golden medal of the Accademia Nazionale delle Scienze detta dei XL (1911)

Eugenio Elia Levi (18 October 1883 – 28 October 1917) was an Italian mathematician, known for his fundamental contributions in group theory, in the theory of partial differential operators and in the theory of functions of several complex variables. He was a younger brother of Beppo Levi and was killed in action during First World War.

Work

Research activity

He wrote 33 papers, classified by his colleague and friend Mauro Picone according to the scheme reproduced in this section.

Group theory

He wrote only three papers in group theory: in the first one, discovered what is now called Levi decomposition, which was conjectured by Wilhelm Killing and proved by Élie Cartan in a special case.

Function theory

In the theory of functions of several complex variables he introduced the concept of pseudoconvexity during his investigations on the domain of existence of such functions: it turned out to be one of the key concepts of the theory.

Boundary value problems

His researches in the theory of partial differential operators lead to the method of the parametrix, which is basically a way to construct fundamental solutions for elliptic partial differential operators with variable coefficients: the parametrix is widely used in the theory of pseudodifferential operators.

Calculus of variations

Publications

The full scientific production of Eugenio Elia Levi is collected in reference .

• , reprinted also in, volume I. A a well-known memoir in Group theory: it was presented to the members of the Accademia delle Scienze di Torino during the session of April 2, 1905, by Luigi Bianchi.
• . A short note announcing the results of paper .
• . An important paper whose results were previously announced in the short note with the same title. It was also translated in Russian by N. D. Ajzenstat, currently available from the All-Russian Mathematical Portal: .
• . An important paper in the theory of functions of several complex variables, where the problem of determining what kind of hypersurface can be the boundary of a domain of holomorphy.
• . Another important paper in the theory of functions of several complex variables, investigating further the theory started in .
• . His "Collected works" in two volumes, collecting all the mathematical papers of Eugenio Elia Levi in a revised typographical form, both amending typographical errors and author's oversights. A collection of all his published papers (in their original typographical form), probably an unordered uncorrected collection of offprints, is available online at the Internet Archive: .

See also

• Pseudoconvexity
• Levi decomposition
• Parametrix
• Several complex variables

References

Biographical and general references

• . Wide source of unpublished manuscript documents of and about E.E. Levi. A short presentation could be found on EGEA website
• . An ample biographical paper (nearly 40 pages) on Beppo Levi: an earlier version of it was published as . It gives many useful information on the family and on the relationship between the two Levi brothers.
• . The relation of Enrico D'Ovidio, Luigi Bianchi and Vito Volterra motivating their decision for the awarding of the golden medal of the Accademia Nazionale delle Scienze detta dei XL to Eugenio Elia Levi.
• . The most widely known biographical reference on Eugenio Elia Levi, written by Guido Fubini and Gino Loria.
• . A pamphlet containing the commemoration of Eugenio Elia Levi pronounced by Gino Loria at the University of Genova on May 29, 1918.
• .
• . A commemorative paper on Eugenio Elia Levi written by Mauro Picone and included in the first volume of his Opere .
• .
• . Available from the website of the Società Italiana di Storia delle Matematiche. An ample historical paper written by Francesco Tricomi to commemorate all Italian mathematicians who worked during the first century of the Italian State.
• .

External links

• .
• . The biographical entry about Eugenio Elia Levi in the "Dizionario Biografico degli Italiani (Biographical Dictionary of Italians)" section of the Enciclopedia Treccani.
• . Available from the Edizione Nazionale Mathematica Italiana.