Entry requirements

120 credit points and Topology, Functional Analysis I, Measure and Integration Theory I

Learning outcomes

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

• give an account of the basic theory for Sobolev spaces;
• use functional analytic methods for treating differential and integral equations;
• give an account of the properties of various classes of operators;
• use category theorems for qualitative conclusions;
• solve simple problems about operators in Banach and Hilbert spaces.

Content

Locally convex topological vector spaces, seminorms. Sobolev spaces, Sobolev’s embedding theorem. Banach algebras and spectral theory for bounded selfadjoint operators in Hilbert spaces.

Briefly about interpolation of operators. Briefly about various classes of operators (compact, Hilbert–Schmidt, trace classes, etc.)

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.