Felice Casorati (17 December 1835 – 11 September 1890) was an Italian

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, mathematical structure, structure, space, Mathematica ...

who studied at the

University of Pavia The University of Pavia (, UNIPV or ''Università di Pavia''; ) is a university located in Pavia, Lombardy, Italy. There was evidence of teaching as early as 1361, making it one of the List of oldest universities in continuous operation, oldest un ...

. He was born in

Pavia Pavia ( , ; ; ; ; ) is a town and comune of south-western Lombardy, in Northern Italy, south of Milan on the lower Ticino (river), Ticino near its confluence with the Po (river), Po. It has a population of c. 73,086. The city was a major polit ...

and died in Casteggio. He is best known for the Casorati–Weierstrass theorem in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

. The theorem, named for Casorati and Karl Theodor Wilhelm Weierstrass, describes the remarkable behaviour of

holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex de ...

s near essential singularities, which is that every holomorphic function gets values from any complex

neighbourhood A neighbourhood (Commonwealth English) or neighborhood (American English) is a geographically localized community within a larger town, city, suburb or rural area, sometimes consisting of a single street and the buildings lining it. Neighbourh ...

, in any neighbourhood of the singularity. The Casorati matrix is useful in the study of linear difference equations, just as the

Wronskian In mathematics, the Wronskian of ''n'' differentiable functions is the determinant formed with the functions and their derivatives up to order . It was introduced in 1812 by the Polish mathematician Józef Wroński, and is used in the study of ...

is useful with

linear differential equations In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written in the form a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) where and are arbi ...

. It is calculated based on n functions of the single input variable.

Works

* , available at Gallica (also a
GDZ
. Freely available copies of volume 1 of his best-known

monograph A monograph is generally a long-form work on one (usually scholarly) subject, or one aspect of a subject, typically created by a single author or artist (or, sometimes, by two or more authors). Traditionally it is in written form and published a ...

, the only one ever published. * Casorati, Felice – Proprietà cardinali degli strumenti ottici anche non centrati, 1872 – BEIC 12019258.jpg, ''Le proprietà cardinali degli strumenti ottici anche non centrati'', 1872

External links

* * 1835 births 1890 deaths 19th-century Italian mathematicians Italian mathematical analysts Scientists from Pavia Mathematicians from the Austrian Empire {{Italy-mathematician-stub