Felice Casorati (mathematician)

Encyclopedia

**Felice Casorati**was an Italian

Italy

Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

best known for the Casorati-Weierstrass theorem in complex analysis

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 useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...

. He was born in Pavia

Pavia

Pavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...

and died in Casteggio

Casteggio

Casteggio is a comune in the Province of Pavia in the Italian region Lombardy, located about 61 km south of Milan and about 25 km south of Pavia...

.

The theorem, named for Casorati and Karl Theodor Wilhelm Weierstrass, describes the remarkable behavior of holomorphic function

Holomorphic function

In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain...

s near essential singularities

Essential singularity

In complex analysis, an essential singularity of a function is a "severe" singularity near which the function exhibits extreme behavior.The category essential singularity is a "left-over" or default group of singularities that are especially unmanageable: by definition they fit into neither of the...

.

The Casorati matrix is useful in the study of linear difference equations

Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms....

, just as the Wronskian

Wronskian

In mathematics, the Wronskian is a determinant introduced by and named by . It is used in the study of differential equations, where it can sometimes be used to show that a set of solutions is linearly independent.-Definition:...

is useful with linear differential equations. It is calculated based on n functions of the single input variable.

## Works

, available at Gallica (also at GDZ). Freely available copies of volume 1 of his best known monographMonograph

A monograph is a work of writing upon a single subject, usually by a single author.It is often a scholarly essay or learned treatise, and may be released in the manner of a book or journal article. It is by definition a single document that forms a complete text in itself...

, the only one ever published.