Specialised Course on Distribution Theory
Official Course Description
This course is an introduction to pseudo-differential operators and para-differential calculus with applications to partial differential equations. Pseudo-differential operators generalize linear differential operators with smooth coefficients and e.g. also include solution operators to some partial differential equations. These operators are defined using the Fourier transform and a function called the symbol of the operator. We will study the connection between the operator and the symbol (e.g. conditions on the symbol which guarantee that the operator is bounded between different function spaces). We will also develop a ”calculus” which e.g. describes what happens on the symbol side when two operators are composed. In the second half of the course, we will move on to para-differential calculus. This is an extension of the pseudo-differential calculus which allows symbols of limited regularity and which can be used to study nonlinear partial differential equations.