# Functional Analysis (FunkAn)

### Course 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 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.
Education

MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject

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.

5 hours lectures (2+2+1) and 3 hours of exercises per week for 8 weeks.

Analyse 0 (An0), Analyse 1 (An1), Analyse 2 (An2) or Lebesgueintegralet og målteori (LIM), and Topology (Top).

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course
ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Two written assignments and a Final 3 hours written exam, under invigilation. Each of the written assignments count 25% towards the final grade; the students will be given 5 days to work on each. The Final written exam counts 50% towards the final grade, and it takes place in week 9.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
##### Criteria for exam assessment

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

Single subject courses (day)

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

### Kursusinformation

Language
English
Course number
NMAK10008U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 2
Schedulegroup
A
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Magdalena Elena Musat   (5-747c7a687b4774687b6f35727c356b72)
Phone +45 35 32 07 45, office 04.2.05
Saved on the 28-02-2022

### Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students