Carlo Severini (10 March 1872 – 11 May 1951) was an
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
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 ...
: he was born in
Arcevia
Arcevia is a '' comune'' in the province of Ancona of the region of Marche, central-eastern Italy.
History
According to tradition, Arcevia originates from a Gallic settlement anterior to the Roman conquest of Italy; following that, it became ...
(
Province of Ancona
The province of Ancona ( it, provincia di Ancona) is a province in the Marche region of central Italy. Its capital is the city of Ancona, and the province borders the Adriatic Sea. The city of Ancona is also the capital of Marche.
To the north, ...
) and died in
Pesaro. Severini, independently from
Dmitri Fyodorovich Egorov, proved and published earlier a proof of the theorem now known as
Egorov's theorem
In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, a ...
.
Biography
He graduated in
Mathematics from 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 continu ...
on November 30, 1897: the title of his "
Laurea
In Italy, the ''laurea'' is the main post-secondary academic degree. The name originally referred literally to the laurel wreath, since ancient times a sign of honor and now worn by Italian students right after their official graduation ceremony ...
"
thesis
A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: ...
was "''Sulla rappresentazione analitica delle funzioni arbitrarie di variabili reali''". After obtaining his
degree, he worked in
Bologna
Bologna (, , ; egl, label=Emilian language, Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 1 ...
as an assistant to the chair of
Salvatore Pincherle
Salvatore Pincherle (March 11, 1853 – July 10, 1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "''Unio ...
until 1900. From 1900 to 1906, he was a senior high school teacher, first teaching in the
Institute of Technology
An institute of technology (also referred to as: technological university, technical university, university of technology, technological educational institute, technical college, polytechnic university or just polytechnic) is an institution of te ...
of
La Spezia and then in the
lyceum
The lyceum is a category of educational institution defined within the education system of many countries, mainly in Europe. The definition varies among countries; usually it is a type of secondary school. Generally in that type of school the t ...
s of
Foggia and of
Turin
Turin ( , Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The ...
;
[According to .] then, in 1906 he became full professor of
Infinitesimal Calculus at the
University of Catania
The University of Catania ( it, Università degli Studi di Catania) is a university located in Catania, Sicily. Founded in 1434, it is the oldest university in Sicily, the 13th oldest in Italy, and the 29th oldest university in the world. With a ...
. He worked in
Catania until 1918, then he went to the
University of Genova
The University of Genoa, known also with the acronym UniGe ( it, Università di Genova), is one of the largest universities in Italy. It is located in the city of Genoa and regional Metropolitan City of Genoa, on the Italian Riviera in the Liguri ...
, where he stayed until his retirement in 1942.
Work
He authored more than 60 papers, mainly in the areas of
real analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...
,
approximation theory and
partial differential equations, according to . His main contributions belong to the following fields of
mathematics:
Approximation theory
In this field, Severini proved a generalized version of the
Weierstrass approximation theorem
Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...
. Precisely, he extended the original result of
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...
to the class of
bounded locally integrable function In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition. The importance of such functions lies ...
s, which is a class including particular
discontinuous functions as members.
Measure theory and integration
Severini proved
Egorov's theorem
In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, a ...
one year earlier than
Dmitri Egorov
Dmitri Fyodorovich Egorov (russian: Дми́трий Фёдорович Его́ров; December 22, 1869 – September 10, 1931) was a Russian and Soviet mathematician known for contributions to the areas of differential geometry and mathematic ...
in the paper , whose main theme is however
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
orthogonal functions In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the ...
and their properties.
Partial differential equations
Severini proved an
existence theorem
In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase " there exist(s)", or it might be a universal statement whose last quantifier is existential ...
for the
Cauchy problem
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value prob ...
for the
non linear hyperbolic partial differential equation
In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n-1 derivatives. More precisely, the Cauchy problem can be ...
of first order
:
assuming that the Cauchy data
(defined in the
bounded interval
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers satisfying is an interval which contains , , and all numbers in between. Other ...