Entry requirements

120 credit points including at least 60 credit points Mathematics and Linear Algebra II and Transform Methods

Learning outcomes

In order to pass the course (grade 3) the student should be able to

• use basic functional analytic formalism in normed spaces;
• use ON-systems and orthogonal projections in Hilbert spaces;
• solve simple problems about the weak topology;
• solve simple Hilbert space spectral theory problems.

Content

Topology in metric spaces. Normed spaces. Banach spaces, inner product spaces, Hilbert spaces. Linear maps. Basic functional analytic theorems: Hahn–Banach’s theorem, Banach–Steinhaus’ theorem, the open map and the closed graph theorems. Weak convergence. Operators on Hilbert spaces. Geometry in Hilbert spaces. The spectral theory for compact symmetric operators.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.