Eugenio Elia Levi

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Eugenio Elia Levi
Eugenio Elia Levi.jpg
Born (1883-10-18)18 October 1883
Torino, Italy
Died 28 October 1917(1917-10-28) (aged 34)
Cormons, Italy
Nationality Italian
Fields Group theory
Several complex variables
Partial differential operators
Institutions Scuola Normale Superiore
University of Genoa
Alma mater Scuola Normale Superiore
Academic advisors Luigi Bianchi
Ulisse Dini
Known for Levi decomposition
Notable 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 the younger brother of Beppo Levi and died in the First World War.


Research activity[edit]

He wrote 33 papers, classified by his colleague and friend Mauro Picone[1] according to the scheme reproduced in this section.

Differential geometry[edit]

Group theory[edit]

He wrote only three papers in group theory: in the first one, Levi (1905) discovered what is now called Levi decomposition, which was conjectured by Wilhelm Killing and proved by Élie Cartan in a special case.

Function theory[edit]

In the theory of functions of several complex variables he introduced the concept of pseudoconvexity[2] during his investigations on the domain of existence of such functions: it turned out to be one of the key concepts of the theory.

Cauchy and Goursat problems[edit]

Boundary value problems[edit]

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[edit]


See also[edit]


  1. ^ This section is mainly based on the survey article by Picone (1959) included in Levi's "Opere (Collected works)", describing his researches briefly but comprehensively; occasionally, also the comments of Guido Fubini in (Fubini & Loria 1917) are taken into account.
  2. ^ See the two well known papers (Levi 1910) and (Levi 1910): note that Levi deals with functions of two complex variables, but his calculations can be extended to functions with any finite number of variables, as he explicitly states. Note also that Levi, following a then well established practice, does not uses Wirtinger derivatives.


External links[edit]