Bachelor's Thesis in Harmonic Analysis and Operator Theory
On this page you will find information specific for the courses SA114X and SA120X, with specialization towards Harmonic Analysis and Operator Theory.
Prerequisities for writing a bachelor's thesis in Harmonic Analysis and Operator theory are covered by the course SF1677 - Foundations of Analysis . The course is given every spring. It is recommended that the student have taken this course before taking the courses SA114X or SA120X, with specialization towards Harmonic Analysis and Operator theory.
If you are interested in writing a bachelor's thesis in Harmonic Analysis and Operator theory you are encouraged to take contact as soon as possible to discuss possible projects and get advice on needed background material for their particular project.
Suggestions for projects
Dirichlet series is a generalization of complex power series, where powers 1/ns, where n runs over positive integers, are sum up with some coefficients. They possess many interesting analytic properties as well as they have deep connections with number theory.
Reproducing kernel Hilbert spaces
A reproducing kernel Hilbert space is a Hilbert space of functions such that point evaluations are bounded functionals. There is a canonical correspondence between such spaces and positive-definite matrices of possibly infinite dimension. This correspondence leads to interesting relationships between algebraic properties of matrices and analytic properties of Hilbert spaces.
The shift operator is among most important operators in harmonic analysis and operator theory. The study of its properties is closely connected with different areas of analysis such as stationary stochastic processes, spaces of analytic functions, model theory of operators etc.
Contact persons
Please contact Håkan Hedenmalm if you are interested in writing a bachelor's thesis.