Bachelorprojects Function spaces
Several topics are possible, related to the course Function spaces. These topics typically consider orthogonal polynomials,
differential equations, fourier transformations or (generalizations of) complex analysis. A topic of choice can be composed
A typical example of a topic is
Dunkl operators in dimension 2
Dunkl operators are generalizations of partial derivatives which are a linear combination
of differential and difference operators. These operators allow us for example to define a Laplacian which is only invariant
under a finite reflection-group and not under the full orthogonal group. The goal of this project is to study these operators
in dimension 2, voor all dihedral groups. In particular, the Dunkl operators in this situation can be used to define a
generalized Cauchy-Riemann operator, of which we plan to determine its kernel explicitly in terms of known orthogonal
polynomials. (This project has an analytical, a geometrical and a computational component).
These projects are under the guidance of Prof. Dr. Hendrik De Bie.