Jan Mikusiński (April 3, 1913 Stanisławów – July 27, 1987 Katowice) was a Polish mathematician based at the University of Wrocław known for his pioneering work in mathematical analysis. Mikusiński developed an operational calculus – known as the Calculus of Mikusiński (MSC 44A40), which is relevant for solving differential equations. His operational calculus is based upon an algebra of the convolution of functions with respect to the Fourier transform. 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 . He is also well known for Mikusinski's cube and Antosik–Mikusinski theorem, and Mikusinski convolution algebra.
A street in Katowice is named after Mikusiński.
- 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)
- O'Connor, John J.; Robertson, Edmund F., "Jan Geniusz Mikusinski", MacTutor History of Mathematics archive, University of St Andrews.