Functional Analysis II
Syllabus, Master's level, 1MA044
This course has been discontinued.
- Code
- 1MA044
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc, 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
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Locally convex topological vector spaces, seminorms. Sobolev spaces, Sobolev's embedding theorem. Banach spaces 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 and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.