Old projects
Here are some projects I have done during my education.
The texts are in their original form and so are full of
errors. But the contents are still interesting.
In 1997 I wrote a bacholor project about
invariant measures on locally compact groups.
It is written in danish and a copy of the project can be downloaded
here. As part
of a course in communicating
mathematics at LSU I wrote an
english version,
just containing
the existence and uniqueness of the Haar measure on locally compact
groups.
Later I wrote a
project
in english about convolution on Lebesguespaces.
It includes a proof for Young's inequality.
I have also done a project about picture compression using wavelets.
I used Daubechies' wavelets to generate Quadrature Mirror Filters
and then transformed pictures using them. I then cut away small
coefficients and did the inverse transform. The results
were quite good compared to JPEG.
Sources
in C++ and the
report
in gzipped postscript
can be downloaded and used without restrictions.
On May 28, 2003 I handed in my
master's thesis
about uncertainty principles. Uncertainty principles have
had my interest since I studied physics.
After 5 years of studies at Louisiana State University under
Gestur Olafsson I finished my
Ph.D. dissertation and defended on June 26 2009.
The dissertation focuses on the interplay between representation theory
and the theory of Banach spaces of function or distributions.
In particular it suggests a generalization of the coorbit theory by
H.G. Feichtinger and K. Gröchenig.
