Vorlesung „Functional analysis“
Funktional analysis (FA) is a of fundamental importance for the analytical branch of pure mathematics, and in the much of applied and numerical mathematics, e.g. in the theory and numerics of partial differntial equations and integral equations, for optimization and in approximation theory, and also in many branches of stochastics.
At the same time, it plays an important role in physics, in particular in quantum mechanics. Many parts of funktional analysishave been developped at the beginning of the twentith century, to lay solid mathematical foundations for the ideas of the physicists. As a principle: quanten mechanical systems are described by a Hilbert space, measurments by application of a self-adjoint operator, the time evolution via application of an operator which has to be inserted in a function.
FA is (after Diff I and Diff II) the completion of the analytical basic education of any mathematician.
The subject of the course FA is the theory of normed vector spaces, in particular of Hilbert spaces, and the continuous linear maps between these.
We will cover in particular
The course is planned to be held in english, on mutual agreement we could also switch to German (or French or Italian)