Course syllabus

Funktionalanalys och harmonisk analys
Functional Analysis and Harmonic Analysis

FMA260, 7,5 credits, A (Second Cycle)

Valid for: 2015/16
Decided by: Education Board B
Date of Decision: 2015-04-16

General Information

Elective for: F5, F5-tf, F5-bs, F5-ss, Pi4-bs, Pi4-ssr
Language of instruction: The course will be given in English on demand


Functional analysis and harmonic analysis are fundamental tools in many mathematical applications (e.g., in field theory, solid mechanics, control theory, signal processing) and in mathematical statistics and numerical analysis. The aim of the course is to convey knowledge about basic concepts and methods, and to give the ability, both to follow discussions where these are used and to independently solve mathematical problems which arise in the applications. An important goal of the course is also to develop a power of abstraction which makes it easier to see analogies between problems from apparently different fields.

Learning outcomes

Knowledge and understanding
For a passing grade the student must



Competences and skills
For a passing grade the student must




Functional analysis: norms and approximation,  completeness, compactness, function spaces, Hilbert spaces, orthogonality and orthogonal systems, linear operators, spectral theory. Dual spaces and Hahn-Banach.

Harmonic analysis: the Fourier transform and Sobolev spaces. Uncertainty relations, the sampling theorem, Fourier transforms and analytic functions, the Hilbert transform.

Examination details

Grading scale: TH
Assessment: Written and/or oral test, to be decided by the examiner.


Required prior knowledge: FMA021 Applied Mathematics and FMA120 Matrix Theory.
The number of participants is limited to: No

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst,
Teacher: Pelle Pettersson,
Course homepage: