About me:

I am a professor of mathematics, and I have taught at the University of Iowa since 1984. Before that, I taught at Stanford University, at the University of Pennsylvania, and at Aarhus University, Denmark. (See CV.)

============================== A math story: =============================

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
color, 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. If I heard them mentioned later, I might
have been slightly amused, but no more than that. Perhaps not before wavelet
math, or rather my interests in wavelets in the late 1980ties, did all of that
stuff about frequency bands gradually resurface, from out of a mist, recalled
from the back reaches of my mind. So it was only after I grew up and matured
myself, that I found that these subband filters define operators in Hilbert
space which satisfy all kinds of abstract relations, now known as Cuntz- and
Cuntz-Krieger relations, and thought in some circles to have been invented in
1977, by Cuntz, or in 1965 by Dixmier. These are tools from math that I had
gotten involved with in the late 1970ties for completely different reasons. My
impression is that the operator relations that are called the Cuntz relations
in math go way back, probably way back to before I was born; and they are and
have been used every day, and twice on Sundays, ever since, by signal
processing engineers, and others I probably don't even know about. In addition
to their extensive use in several areas of math! Our matrix functions from
math are actually called poly-phase matrices by engineers, and they are
scattering matrices in other circles, and quantum gates in physics. In fact a
lot of the things we do in operator theory are known and used in other fields,
but known under different names, and known in different ways. And important
for different reasons! In any case, they *are* really important, and for all
kinds of good reasons, not least of which is their rediscovery in operator
algebras, and in wavelets. -----------------------------------------------

Palle Jorgensen; Math
University of Iowa
Iowa City, IA 52242 USA

Palle E. T. Jorgensen

This page was last modified on 24 August 2006 by Brian Treadway.

Back to Palle Jorgensen's home page