Course syllabus

Funktionalanalys och harmonisk analys
Functional Analysis and Harmonic Analysis

FMAN80, 7,5 credits, A (Second Cycle)

Valid for: 2023/24
Faculty: Faculty of Engineering, LTH
Decided by: PLED F/Pi
Date of Decision: 2023-04-18

General Information

Elective for: F5, F5-tf, F5-bs, F5-ss, Pi4-bs, Pi4-ssr, MMSR2
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 in the subject, 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, compact operators and self-adjoint operators. Spectral theory. Dual spaces and Hahn-Banach's theorem.

Harmonic analysis: The Fourier transform. Sobolev spaces and the Sobolev embedding theorem.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Take-home exam followed by an oral exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.


Assumed prior knowledge: FMAN55 Applied Mathematics and FMAN70/FMAN71 Matrix Theory.
The number of participants is limited to: No
The course overlaps following course/s: FMA260

Reading list

Contact and other information

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