Prof. Jan Mikusiński was a Polish

Poland

Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...

 mathematician known for his pioneering work in mathematical analysis

Mathematical analysis

Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

. Mikusiński developed an operational calculus

Operational calculus

Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation.-History:...

 - 44A40 Calculus of Mikusiński, which is relevant for solving differential equations. His operational calculus is based upon an algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

 of the convolution of functions with respect to the Fourier transform

Fourier transform

In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

. From the convolution product he goes on to define what in other contexts is called the field of fractions or a quotient field. These ordered pairs of functions Mikusiński calls operators - Mikusiński Operator , 44A40 . He's also well known for Mikusinski's cube and Antosik–Mikusinski theorem, Mikusinski convolution algebra etc.

External links

• Caricature of Jan Mikusinski
• Rachunek operatorów http://matwbn.icm.edu.pl/kstresc.php?tom=30&wyd=10&jez= (Operational Calculus in Polish)

part. 1 http://matwbn.icm.edu.pl/ksiazki/sm/sm77/sm7711.pdf
part. 2 http://matwbn.icm.edu.pl/ksiazki/sm/sm77/sm7712.pdf original paper 1944 1983 (English)

• http://ux1.math.us.edu.pl/instytut/historia/mikusinski/mikusinski.html