Jens Gerlach Christensen
Assistant Professor
Department of Mathematics
Colgate University
» Home
» Research
» Presentations
» Old projects
» Activities
» Contact

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 Lebesgue-spaces. 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.