Aim of the course

This course treats Fourier analysis and distribution theory. In Fourier analysis one studies functions on R, R^n, or more general spaces by writing them as linear superpositions of elementary functions. This is very clear in the situation of periodic functions. These may often be expressed as linear superpositions of exponentials with the same period. It is interesting to study the connection between functions and their Fourier transform for its own sake, but it has turned out that Fourier analysis is a powerful tool to handle problems in differential equations, signal analysis, x-ray tomography, etcetera. When one studies the classes of functions that permit Fourier analysis, it soon becomes clear that one should study a larger class of objects, the so called distributions or generalized functions. In this course all these aspects will be dealt with to some extent.

Bachelor mathematics, preferably with introductory functional analysis