# Palle Erik Tikob Jorgensen

### Quick Info

Frederiksberg, Copenhagen, Denmark

**Palle Jorgensen**is a Danish mathematician who worked mainly in America. He has published a large number of papers in both pure and applied mathematics.

### Biography

**Palle Jorgensen**was the son of Soren A W Jorgensen and Gyrit D Baden. Palle's father, Soren Jorgensen, was an electrical engineer, while his mother Gyrit was a mathematics teacher. Palle Jorgensen writes [5]:-

My grandfather on my mother's side, Rasmus Bortmann Tikøb Baden, was a biblical scholar, and he was deeply interested in science. A quote from Pastor Baden that sticks in my mind (I must have been 4 or 5 years old at the time), is this: "Mathematics and physics is the wisdom of God, while the social sciences represent the study of stupidity of Mankind." At this very early age, all three, my mother, father, and Pastor Baden, profoundly influenced my thinking. I always believe that what we learn in the first 5 to 10 years of our lives, has much more of an impact than what comes later. Early influences from my mother include geometry, complex numbers, and Taylor's formula. My mother was extremely good at languages. Perhaps our learning of mathematics has a lot in common with that of languages. With hindsight, I realized that I acquired a facility with three "foreign" languages from my mother; way back in my formative years. At the same time, from listening to my father discuss high-pass and low-pass filters, and long-distance transmission, I picked up fundamentals of signal processing. I am reminded of this signal processing-inspiration in my much later research on wavelet multiresolutions; and I mention it in my Wavelet book from 2002.He went into a little more detail about the influence of his father's work on high-pass and low-pass filters in [4] (see also [2]):-

When I was little, growing up in Denmark, - before kindergarten; only there wasn't any then ..., - so before I heard of 'The Tinder Box', or 'The Ugly Duckling' from the books of Hans Christian Andersen, my father told me about low-pass and high-pass filters. He was a telephone engineer and worked on the filters used in signals transmitted over long cables, just after the war, WWII. The 'high' and 'low' part of the story refers to frequency bands of the sound signals. Not that this meant much to me at the time. Rather, I was fascinated by the pictures in the EE journals that were stacked up on the floor next to me, and I spent hours looking at them [- that was all there was, there on the floor!], so these pictures of filter design, some in colour, occupied me on long Sundays while my dad was building instruments in the living room. Nothing else for me to do! Then, after going to school, I forgot all about my dad's explanation of quadrature mirror filters; no wonder(!!), and they were out of mind for a very long time. I never had any particular reason to think much about them at all, I mean the low-pass frequency bands and all that, but I am sure they in some strange way created a lasting visual impression for me.He wrote about the later influences on him in [5]:-

As a child, from age 11 to 17, in my school-summer breaks, I made trips of my own, hitchhiking, off to youth work-camps abroad, in England, Germany, France, and (a Zionist youth group) in Israel, at kibbutzim. Later in High School and at the University, I was fortunate to have had extremely inspiring teachers; but especially fortunate to have been part of a generation of students with ambitions to excel in mathematics and in the sciences. The closest parallel to High School in Denmark is called Gymnasium. The name of mine was Marselisborg Gymnasium in Aarhus. Denmark tutorial: This was a 3-year programme, and I was blessed with great teachers, in mathematics, in the sciences, and in languages. The curriculum at the time included calculus and linear algebra. (The curriculum has probably been watered down since then.) Another interest of mine from this time includes economics.Jorgensen entered Aarhus University and was awarded a B.A. in 1968, an M.S. in 1970 and a Ph.D. in Mathematics in 1973 for his thesis

*Infinite-dimensional representations of Lie algebras and Lie groups*. There were many important influences on Jorgensen during these years. One was Kiyosi Ito who, although a professor at Kyoto University from 1952 until he retired in 1979, but held a position as professor at Aarhus University in the years 1966-69 while Jorgensen was a graduate student. His thesis advisor at Aarhus was Niels Kristian Skovhus Poulsen who had himself graduated with a Ph.D. in 1970 advised by Irving Segal. Jorgensen writes [5]:-

At Aarhus University, I had great mathematics teachers, and of my fellow mathematics graduate students, more than a handful ended up as professional mathematicians, and at top universities, both in Denmark, and in the USA. An early, and especially inspiring, mathematics teacher of mine, and of my generation, who stands out is Svend Bundgaard. In fact, Professor Svend Bundgaard was still around in the early 1980s when I was then on the faculty in the Mathematics Department at Aarhus University.Let us say a little more about Svend Bundgaard (1912-1984). He was educated at the University of Copenhagen and, after teaching at that university, was appointed to a chair at the newly established Faculty of Science at Aarhus University in 1954. He played a significant role in the expansion of that faculty, particularly the Mathematical Institute, serving as the university's principal in the years 1971-1976. He was also co-founder of the journal

*Mathematica Scandinavica*.

The results from Jorgensen's thesis became part of the later monograph

*Operator commutation relations. Commutation relations for operators, semigroups, and resolvents with applications to mathematical physics and representations of Lie groups*written jointly with Robert T Moore and published in 1984. A review by Derek W Robinson begins [13]:-

In the last thirty years the theory of continuous one-parameter groups and semigroups on Banach spaces has flourished. This theory, which has its historical roots in the dynamical description of quantum-mechanical systems, has subsequently found applications in many fields of mathematics. The main emphasis of this development has been on the analysis of single groups, or semigroups, and their generators. Less effort has been devoted to the study of the analytic structure of families of noncommuting groups and semigroups. Again such problems found their earliest motivation in quantum theory, notably with Heisenberg's formulation in terms of families of noncommuting observables. Problems of this nature form the principal object of the monograph under review and the authors attempt, with some success, to show that analysis of operator commutation relations leads to a unification of diverse areas of mathematics.After the award of his doctorate, Jorgensen was awarded a Danish Natural Science Research Council multi-year post-doctoral fellowship which allowed him to conduct research at universities abroad; foreign travel and international contacts were strongly encouraged. He went to the United States in 1973 and, supported by the fellowship, became a visiting scholar at Princeton University. In 1975 he published his first paper

*Representations of differential operators on a Lie group*which was on Hunt processes on Lie groups. He writes [5]:-

This research was inspired to a large extent by pioneering research of Ed Nelson, and Lars Hörmander.The address on the paper is Department of Mathematics, Princeton University, and the research was sponsored by Odense University, Denmark. The way such postdoctoral fellowships worked in Denmark at this time meant that the funding was from The Danish Natural Science Research Council but the research was sponsored by one or more of the Universities. In Jorgensen's case it was sponsored by Odense University and Aarhus University, Denmark. The paper has the following Acknowledgements:-

The author is indebted to a large number of mathematicians for helpful discussions. He learned about group representations from Niels Skovhus Poulsen. Professor M Reed originally showed interest in the idea of looking at quadratic expressions of infinitesimal generators. Professors V Bargmann, G B Folland, R Goodman, A Klein, R T Moore, E Nelson, E Stein, and A S Wightman have shown interest in various partial results on the way. Professors J J Kohn and F Treves have been helpful with certain differential operator aspects. Valuable improvements have been suggested by the referee. Finally, the author wishes to thank Gregg Zuckerman for many helpful discussions on Lie group representations.Jorgensen's next paper was

*Approximately reducing subspaces for unbounded linear operators*(1976) and, by this time, he had moved to University of Pennsylvania in Philadelphia. He writes in the Acknowledgements:-

It is a pleasure to thank Professor S Sakai for suggesting the problem and for constant encouragement.In [5] Jorgensen explains that his research during his time at the University of Pennsylvania moved in the direction of operator algebras and mathematical physics. It was inspired by Richard V Kadison, his postdoctoral advisor, by Robert T Powers, and by Shôichirô Sakai.

Jorgensen married Soon-Min Park on 4 January 1975. They had three children, Anton Yang Jorgensen (born 24 October 1975), Greta Soon Jorgensen (born 6 September 1978) and Tina Soon Jorgensen.

In the summer of 1976 Jorgensen was an invited member of the NSF Summer Research Institute in Operator Theory at the University of New Hampshire. After working at the University of Pennsylvania until 1977, he moved to Stanford University in that year where he became an Assistant Professor [5]:-

Important influences from the late 1970s include Ralph S Phillips, Hans Samelson, Paul Cohen, Kai Lai Chung, James McGregor, and ... at Stanford. Jorgensen was an assistant professor at Stanford University in that period, and his research was then especially inspired by the Stanford faculty, and graduate students, e.g., Peter Sarnak, at the time.In 1979 Jorgensen petitioned for naturalisation in the district court at San Francisco. He was supported by two witnesses, Soon Min Jorgensen, his wife, and William Arveson (1934-2011) who was a Professor of Mathematics at the University of California, Berkeley, researching on operator algebras. At this time Jorgensen was living on California Street, Mountain View, Santa Clara, California. He was issued with a naturalisation certificate on 24 July 1979. He was awarded a Danish Research Council grant and went to the Mathematics Institute, University of Aarhus, Denmark as an Associate Professor in 1979. For one year he was on leave from Stanford University but he remained at Aarhus after that year, resigning from Stanford. He continued to hold the position at Aarhus until 1983 but in 1982 he spent a year back at the University of Pennsylvania as a Visiting Associate Professor [5]:-

Jorgensen was on the faculty at University of Pennsylvania again in the early 1980s. This time was also the beginning of collaboration with Ola Bratteli which stretched over decades: many joint research publications. Other co-authors in these papers included Derek W Robinson, and George A Elliott.At the end of one year at the University of Pennsylvania, Jorgensen was appointed as a Professor in the Department of Mathematics at the University of Iowa. He resigned his position in Aarhus and was given a year leave of absence from Iowa so that he could continue as a Visiting Associate Professor at the University of Pennsylvania, and start teaching at the University of Iowa in 1984. In the interview [2] he said:-

[At the University of Iowa] I have been teaching most of the undergraduate courses, but in the last few years mostly graduate courses, and I collaborate with colleagues in physics (the theory group) and in engineering (industrial, computer and electrical engineering.) I teach courses in analysis, in functional analysis, in applied mathematics (especially physics, signal and image processing. [My main mathematics interests are] operator theory, functional analysis, dynamical systems, among others. Otherwise my professional interests stretch from mathematics to physics, and from engineering (signal and image processing) and to financial mathematics (stochastic differential equations!) ... I enjoy reading. I also enjoy teaching, giving seminars, and working with students, especially my Ph.D. students.Jorgensen is the author or co-author of at least eleven books (and has been an editor of several more). We give some information about books of which he is an author or co-author at THIS LINK.

A recent biography states [12]:-

[Jorgensen's] publication list includes more than 200 research papers, and 8 books: in mathematics, both pure and applied (operator algebras, and harmonic analysis), and mathematical physics (quantum theory). Palle Jorgensen's research covers a wide spectrum, stochastic processes, white noise analysis, harmonic analysis, applied functional analysis, PDE, dynamical systems, discrete algorithms, applied stochastic analysis, and Jorgensen's research makes connections to a number of applied areas, and he has interacted with colleagues from other departments, both at the university of Iowa, and at other universities around the world. This includes colleagues in departments of physics, engineering (department of computer and electrical engineering), department of statistic and actuarial science (University of Iowa.) Over the past seven years Jorgensen has taught financial mathematics both at the graduate level, as well as an undergrad course in derivative securities. These courses draw students from mathematics, from statistics and actuarial science, from engineering, from economics, and from finance. While at the University of Iowa, Jorgensen has had 24 Ph.D. students, with thesis covering both pure and applied themes.Editorial work which Jorgensen has undertaken includes: editor of

*Acta Applicandae Mathematicae*; editor of the

*Proceedings*of the American Mathematical Society; editor of

*Proyecciones: Revista de Matemática*; editor of the

*Panamerican Mathematical Journal*; editor of the

*Journal of Mathematical Sciences*(new series, Delhi, India); editor of the

*Journal of Applied Mathematics and Computing*, editor of the

*Journal of Basic & Applied Sciences*, editor of

*Complex Analysis and Operator Theory*, and editor of the

*Journal of Nonlinear Functional Analysis*.

Jorgensen was honoured with election to the Danish Academy of Natural Sciences in 1982, the year in which the academy was founded.

### References (show)

- O Christensen, Review: Wavelets through a Looking Glass: The World of the Spectrum by Ola Bratteli and Palle E T Jorgensen,
*Zentralblatt, European Mathematical Society*(2003). http://homepage.divms.uiowa.edu/~jorgen/quick2.pdf - Palle Jorgensen,
*The S-Times, University of Iowa Graduate Student Newsletter*(March-April 2008), 4. - Palle E T Jorgensen,
*University of Iowa*. http://homepage.divms.uiowa.edu/~jorgen/jorgcvw.pdf - P E T Jorgensen, Matrix Factorizations, Algorithms, Wavelets,
*Notices Amer. Math. Soc.***50**(8) (2003), 880-894. - P E T Jorgensen,
*Personal Communications*(26-27 July 2019). - P E T Jorgensen, Bio sketch: Palle Jorgensen, Professor, University of Iowa, USA,
*University of Iowa*. https://math.uiowa.edu/sites/math.uiowa.edu/files/field/cv/Bio%20sketch%20Jorgensen%20NSF%20Spr2019.pdf - P E T Jorgensen, About me,
*University of Iowa*. http://homepage.divms.uiowa.edu/~jorgen/aboutme.html - P E T Jorgensen, Preface,
*Analysis and Probability: Wavelets, Signals, Fractals*(Springer, Berlin-Heidelberg-New York, 2006), vii-viii. - P E T Jorgensen, An apology,
*Analysis and Probability: Wavelets, Signals, Fractals*(Springer, Berlin-Heidelberg-New York, 2006), xv-xvi. - P E T Jorgensen, Complete bibliography,
*University of Iowa*. http://homepage.divms.uiowa.edu/~jorgen/jorgbibl.pdf - J A Packer, Review: Wavelets through a Looking Glass: The World of the Spectrum by Ola Bratteli and Palle E T Jorgensen,
*SIAM Review***46**(2) (2004), 368-372. - Palle E T Jorgensen, PhD, Editorial Board Member, Biography,
*SciTechnol*(2018). https://www.scitechnol.com/editor-profile/Palle_ET_Jorgensen/ - D W Robinson, Review: Operator Commutation Relations, by Robert T Moore and Palle E T Jorgensen (D Reidel, Dordrecht, 1984),
*Mathematical Reviews*MR0746138**(86i:22006)**. - F H Vasilescu, Review: Operator Commutation Relations, by Robert T Moore and Palle E T Jorgensen (D Reidel, Dordrecht, 1984),
*Zentralblatt, European Mathematical Society*. http://homepage.divms.uiowa.edu/~jorgen/Zbl053547020.pdf

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update November 2019

Last Update November 2019