# Franciszek Hugon Szafraniec

### Quick Info

Świętochłowice, Upper Silesia, Poland

**Franciszek Szafraniec**is a Polish mathematician best known for his work in operator theory.

### Biography

**Franciszek Szafraniec**was born in Silesia only a few months after Poland had been invaded by Germany at the start of World War II. Silesia had a population that was divided between German speaking people (mostly in the towns) and Polish speaking people (mainly in the country) and whether it should be part of Germany or part of Poland had been disputed following World War I. Eventually it had been divided with the part in which Szafraniec was born becoming a part of Poland. This part of Silesia had most of Silesia's coal and steel production. The authors of [1] write:-

[Szafraniec's] home town Świętochłowice, mostly inhabited by coal miners as well as steel and zinc workers, has impacted his attitude for the rest of his life. Those common people are valued for their reliability, sincerity and a clear sense of humour. Though the environment he grew up in might seemingly be in contrast to his liberal arts profile education all this together blended in creating a mighty personality of the man we know now.After graduating from secondary school, it was still unclear which topic Szafraniec would study at university. Moreover, it was unclear which university he would study at. Szafraniec's father wanted his son to study in Kraków while his mother would have preferred her son to go to the more local Wrocław University. After some deliberations, a decision was made at the last minute that Szafraniec would apply to study mathematics at the Jagiellonian University in Kraków. He was offered a place and began his undergraduate studies there. He attended lectures by Tadeusz Ważewski who had taught at the Jagiellonian University before World War II and had then returned there after it was liberated in 1945 putting great efforts into restoring the educational system which had been destroyed during the German occupation. Ważewski had built an important seminar at the Jagiellonian University which was mainly devoted to the study of differential equations. He was famed for his topological approach to the study of differential equations, and had obtained remarkable results applying Borsuk's theory of retracts. Szafraniec became a member of Ważewski's school and, after his undergraduate studies, undertook research advised by Ważewski. He was awarded a Master's degree (equivalent to a Ph.D.) in 1968 for a thesis on the theory of differential equations. The papers he wrote while he was undertaking research included:

*On a certain sequence of ordinary differential equations*(1963); (with Andrzej Lasota)

*Sur les solutions périodiques d'une équation différentielle ordinaire d'ordre n*Ⓣ (1966) and (with Andrzej Lasota)

*Application of the differential equations with distributional coefficients to the optimal control theory*(1968).

In fact this paper on control theory marked a change in topic for Szafraniec and the authors of [1] explain how this came about:-

This happened to Szafraniec on a sunny June day in 1968 when he met Wlodzimierz Mlak (1931-1994), also a member of the Ważewski seminar, on the Main Market Square in Kraków. After a long coffee session in a nearby café he got converted to the theory of operators. This way operators entered his mathematical life and, in other words, a seed of operator theory was sowed on the Kraków soil. The passion which both of them had for this branch of mathematics was shared by their students and passed on to subsequent generations of mathematicians. This way Kraków became a vital world centre of modern operator theory. The co-workers and former students of Professor Szafraniec may be found in all major Kraków universities.Let us note that Wlodzimierz Mlak had been a student at the Jagiellonian University with Czeslaw Olech, Zdzisław Opial (1930-1974) and Jan Bochenek (1927-2009), all of whom were appointed as assistants and went on to become professors of mathematics. Szafraniec worked at the Jagiellonian University in Kraków for his whole career. He was awarded his doctorate (equivalent to the habilitation) in 1971 and he became a professor in 1980. The authors of [1] summarise his mathematical contributions:-

Out of his many noticeable results, we mention a few: simplified forms (including the diagonal one) of the boundedness condition in the famous Szokefalvi-Nagy general dilation theory together with related integral representations of exponentially bounded operator-valued functions on abelian *-semigroups (unfortunately often attributed exclusively to a paper by Berg and Maserick, which appeared later), foundations of the theory of unbounded subnormal operators (together with Jan Stochel), new solutions to multidimensional real and complex moment problems (together with Jan Stochel), fresh look on interpolation theory, three term recurrence relations for orthogonal polynomials of several variables (together with Dariusz Cichon and Jan Stochel), and advances in the theory of quantum harmonic oscillators and canonical commutation relations. Professor Szafraniec's interests and activities in the mathematical world, together with his capability of co-operating, bears fruit in many publications which encompasses numerous joint papers with dozens of mathematicians.In fact MathSciNet lists 123 items by Szafraniec (in July 2013), 36 of which are papers presented at conferences. In fact he has attended a vast number of conferences, from China to Mexico and from Chile to South Africa, all of which enriched his main research interest in Hilbert space methods. To illustrate the conferences at which he has spoken and the invited talks he has given at these conferences we give a few examples. At the 1997 workshop 'Special functions and differential equations' held at Madras (now Chennai) in India, he gave the talk

*The quantum harmonic oscillator in*$L^{2}(\mathbb{R})$ in which he introduced the Hilbert-space model of the quantum harmonic oscillator couple of the creation and annihilation operators, he obtained some new interrelations between these operators. At the conference 'Topological algebras, their applications, and related topics' held in Bedlewo, Poland in 2005 he gave the lecture

*Subnormality and cyclicity*. In the same year at the University of Vaasa in Finland he gave the lecture

*A matrix algorithm towards subnormality of unbounded operators*at the 'Algorithmic Information Theory Conference'. In 2006 he attended two conferences, 'Operator theory and indefinite inner product spaces' at the Vienna University of Technology, Vienna, Austria and 'Operator theory in Krein spaces and nonlinear eigenvalue problems' at the Technical University of Berlin, Germany. At the first he gave the lecture

*On normal extensions of unbounded operators. IV. A matrix construction*while at the second he gave the lecture

*Bounded normal operators in Pontryagin spaces*. The first of these when written up for the proceedings became the fourth in a series of papers

*On normal extensions of unbounded operators*some of which were written with Jan Stochel, one of his colleagues at the Jagiellonian University. In fact Szafraniec has written 24 joint papers with Jan Stochel (as of July 2013). Szafraniec has been as editor for the Proceedings of the semester long workshop

*Linear operators*held in Warsaw in the Spring of 1994. He has also been an editor of the 2012 monograph

*Operator methods for boundary valve problems*to which he contributed the chapter

*Naimark dilations and Naimark extensions in favour of moment problems*.

Szafraniec retired from his professorship at the Jagiellonian University in 2010 when he reached the age of seventy. A conference 'Functions and Operators' was held in Kraków in 2010 to celebrate his 70th birthday.

### References (show)

- D Cichon, L Littlejohn and J Stochel, Franciszek Hugon Szafraniec: A Scholar of Eminence,
*Complex Anal. Oper. Theory***6**(3) (2012), 529-531.

### Additional Resources (show)

Other websites about Franciszek Szafraniec:

Written by J J O'Connor and E F Robertson

Last Update October 2013

Last Update October 2013