# NMAK10008U  Functional Analysis (FunkAn)

Volume 2014/2015
Education
MSc Programme in Mathematics
Content

This course will cover a number of fundamental topics within the area of Functional Analysis. These topics include:

• Banach spaces: The Hahn-Banach theorem, including its versions as separation theorem, weak and weak* toplogies, the Banach-Alaoglu theorem, fundamental results connected to the Baire Category theory (the open mapping theorem, the closed graph theorem and the Uniform Boundedness Principle), as well as and convexity topics, including the Krein-Milman theorem and the Markov-Kakutani fixed point theorem.
• Operators on Hilbert spaces, Spectral theorem for self-adjoint compact operators.
• Fourier transform on R^n and the Plancherel Theorem.
• Radon measures and the Riesz representation theorem for positive linear functionals.
Learning Outcome

After completing the course, the student will have:

Knowledge about the subjects mentioned in the description of the content.

Skills to solve problems concerning the material covered.

The following Competences:

• Have a good understanding of the fundamental concepts and results presented in lectures, including a thorough understanding of various proofs.
• Establish connections between various concepts and results, and use the results discussed in lecture for various applications.
• Be in control of the material discussed in the lectures to the extent of being able to solve problems concerning the material covered.
• Be prepared to work with abstract concepts (from analysis and measure theory).
• Handle complex problems concerning topics within the area of Functional Analysis.

Analyse 0 (An0), Analyse 1 (An1), Analyse 2 (An2), and Mål- og integralteori (MI).
5 hours lectures (2+2+1) and 3 hours of exercises per wek for 8 weeks..
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Two mandatory sets of exercises.
Marking scale
Censorship form
External censorship
Re-exam
Oral examination with 30 minutes preparation.
##### Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

• Category
• Hours
• Lectures
• 40
• Preparation
• 116
• Exam
• 26
• Theory exercises
• 24
• Total
• 206