Jan Mikusiński

Jan Mikusiński ( born April 3, 1913 in Stanisławów, † 27 July 1987 in Katowice ) was a Polish mathematician who is known for his contributions to the operational calculus in the analysis.

Life and work

Mikusiński studied at the University of Poznan ( completion in 1937 ). During the Second World War he worked as many Polish mathematician in a university in the underground. In 1945 he received his doctorate in Krakow at Tadeusz Ważewski ( Sur un problème d' interpolation pour les intégrales of differential équations linéaires ) and then was a lecturer in Wroclaw (1948 ), Warsaw (1955) and Katowice. In 1955 he habilitated. In the 1960s, he headed the Mathematical Institute of the Polish Academy of Sciences in Katowice newly established.

Mikusiński is known for the development of an eponymous calculus of differential and integral operators, which is partly powerful than the distribution calculus of Laurent Schwartz or detectable in the theory of Laplace transform operators. He uses the convolution operator of the Fourier transform as a product. He wrote in 1953 the book operational calculus about it. His work was a further contribution to give the operator calculus of Oliver Heaviside 19th centuries, a mathematically rigorous basis.

He holds honorary doctorates from the University of Rostock.

Writings

• An Introduction to Analysis -From Number to Integral. Wiley 1993
• The Operational Calculus. Pergamon Press, Oxford 1983
• Operational calculus. German VEB Verlag der Wissenschaften, Berlin 1957.
• The Bochner integral. Birkhäuser 1978.
• With Piotr Antosik, Roman Sikorski: Theory of distributions - the sequential approach. Elsevier 1973.
• Stanisław Hartman: The theory of Lebesgue Measure and Integration. Pergamon Press, Oxford 1961.