Discrete differential operators for periodic and two-periodic time functions

Tadeusz Sobczyk was born (1944) and educated in Poland. He received MSc, PhD and Dr Habil (DSc) in Electrical Engineering from the Faculty of Electrical Engineering, Automatics and Electronics at the University of Mining and Metallurgy, Cracow, in 1967, 1974 and 1977, respectively, and the scientific title of a Professor in 1991 from the President of Poland. In 2000, he was awarded the honorary title Doctor Honourees Causa by the Russian Academy of Sciences. In 1991-2015 was a member of the Committee of Electrical Engineering of the Polish Academy of Science. He worked at the University of Mining and Metallurgy in Cracow (1967-1989) and in the Cracow University of Technology (1989-2017) at the faculty of Electrical and Electronics Engineering. In the years 1993-1999, he was the Dean of this Faculty and in 1991-2013 Director of the Institute on Electromechanical Energy Conversion and the head of the Chair of Electrical Machines in this Institute. From 2017 he is Senior Professor of the Cracow University of Technology. In the years 2000-2007 he worked at the Institute of Electrical Engineering in Warsaw as a head of the Division of Fundamental Research. His main research fields are electromechanical energy conversion, electrical machines and electric energy transformation by power electronic systems. He has published a book Methodological aspects of mathematical modelling of induction machines (in Polish) and app. 270 scientific papers in Polish and international journals and proceedings of conferences.

Michał Radzik was born (1978) and educated in Poland. He received the MSc and PhD in Electrical Engineering from the Faculty of Electrical and Computer Engineering at Cracow University of Technology in 2003 and 2011, respectively. In 2008, he graduated in PhD Studies at the Faculty of Mechanical Engineering. He works at the State Higher Vocational School in Nowy Sącz in the Technical Institute. His main research field is electrical machines. He has published 19 scientific papers in Polish and in international journals and conference proceedings.

Natalia Radwan-Pragłowska was born (1989) and educated in Poland. She received the MSc degree in Electrical Engineering from the Faculty of Electrical and Computer Engineering at the Cracow University of Technology in 2013. She works at Cracow University of Technology in the Institute of Electromechanical Energy Conversion. Her main research field is electrical engineering. She has published nine scientific papers in Polish journals and conference proceedings.