Krystyna Skórnik, Assistant Professor
Ph. D. January 1971 – at the Silesian University in Katowice for the doctor thesis “Hereditarily Periodic dstributions”. The Doctor Thesis was supervised by Professor Jan Mikusiński.
Professional interests:
Mikusiński’s operational calculus and theory of distributions – Mikusiński’s sequentional approach.
Applications of Mikusiński’s operational calculus to the theory of linear differential equations and
to the theory of special functions as well as to obtaining some functional relations with orthogonal polynomials.
Different kinds of derivatives, eg. local derivatives, Sobolev’s derivatives, tempered derivatives of nonnegative order.
Publications:
I am the author (or co-author) of more then 60 publications, articles in prestigious Polish and foreign journals, 2 text-books (in Polish) for students of the Silesian Technical University. I am the co-author (with H.-J.Glaeske, A.P. Prudnikov) of the book: “Operational Calculus and Related Topics”, Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York, 2006. I was the editor of the anniversary volume “Half of the century of mathematics in Upper Silesia”, Publishing House of the Silesian University in Katowice, 2003.
Hereditarily periodic distributions, Studia Math. 43(1972), 245 – 272.
On tempered integrals and derivatives of a class of generalized functions, Dokl. Akad. Nauk SSSR 254 (1980), No 5, 1085 – 1087.
On local derivatives, Ann. Pol. Math. 41 (1983), 283 – 292.
Sobolev’s and local derivatives, Studia Math. 77 (1984), 509 – 517.
On functions with vanishing local derivatives, Ann. Pol. Math. 47 (1986), 179 – 188.
A remark on the operational exponential functions, with W. Kierat, Bull. Pol. Ac.: Math. 35(1987), 383 – 386.
A remark on tempered integrals and tempered derivatives, in the book: Generalized Functions and Convergence, editors P. Antosik & A. Kamiński, Singapore (1990), 219 – 222.
A remark on solutions of Laguerre differential equation, Dissertationes, with W. Kierat, Math. Vol. 340 (1995), 137 – 141.
Remarks on convolution products of distributions, with W. Kierat, Integral Transform and Special Functions, Proceedings of the Conference Different Aspects of Differentiability, II, Vol. 4, No 1-2 (1996), 97 – 102.
Factoring and splitting of s-differential equations in the field of Mikusiński, with J. Wloka, Integral Transform and Special Functions, Vol. 4, No 3 (1996), 263 – 274.
Some remarks concerning the Bessel equation, with J. Wloka, Integral Transforms and Special Functions, Vol. 5, No 1-2(1997), No 1-2, 153 – 160.
m-Reduction of ordinary differential equations, with J. Wloka, Colloquium Mathematicum, Vol. 78, No 2 (1998), 195 – 212.
An application of the Mikusiński operational calculus un the theory of controllability, with W. Kierat, Integral Transforms and Special Functions, Vol. 7, No 1-2(1998), 159 – 162.
Mikusiński’s operational calculus and its applications, Fractional Calculus and Applied Analysis, Vol. 2, No 4(1999), 509 – 528.
Mean-periodic operational calculi, with I.H. Dimovski, Banach Center Publication, Proceedings of the Conference “Algebraic Analysis and Related Topics”, Vol. 53(2000), 105 – 112.
Mean-periodic operational calculi. Singular cases, with I.H. Dimovski, Fractional Calculus and Applied Analysis, Vol. 4, No 2(2001), 237 – 243.
Generalized Functions and the Theory of Convergence in the Katowice Branch of the Institute of Mathematics of the Polish Academy of Sciences, with P. Antosik, in the volume “Half of the Century of Mathematics in Upper Silesia”, editor K. Skórnik, UŚl. Katowice 2003, 125 - 153.
I have participated in organization of numerous scientific conferences, including organizing international conferences “Different Aspect of Differentiability” (1993, 1995) and “Algebraic Analysis and Related Topics” (1999) together with Prof. Danuta Przeworska- Rolewicz, at the Institute of Mathematics of the Polish Academy of Sciences in Warsaw .
For many years I have organized mathematical competitions for secondary school pupils, organized and worked for the mathematical circles, organized scientific lectures for secondary school students and teachers in the Silesia region.
Memberships:
Since 1963 - Member of the Polish Mathematical Society.
Since 1995 till now - Chairperson of the Polish Mathematical Society, Uppersilesian Branch.
Medal of 50 years of Mathematical Olympiad,
Medal of National Commission on Education (no 98831).
e-mail <skornik@us.edu.pl>