Functional Analysis 1 (WS 23/24)

In this course, the basic concepts and results of functional analysis are treated. In particular, this is done in with respect to applications in the theory of differential operators and spectral analysis.

Topics are e.g. elementary theory of Banach- and Hilbersspaces (L^p-spaces, duality, linear operators, Theorem of Hahn-Banach; Baire Category Theorem and some corollaries, in particular the Banach-Steinhaus-Theorem; orthogonal projections and orthonormal bases in Hilbert spaces), compact, bounded and unbounded linear operators (domain, graph, adjoint, spectrum, resolvent, compact operators, convergence, functional calculus of self adjoint operators), weak topologies and Banach-Alaouglu-Theorem, Frechet spaces of differentiable functions, distributions and tempered distributions with test functions, continuous linear maps on distributions, Fouriertransformation of distributions,