Course Syllabus for

Functional Analysis and Harmonic Analysis
Funktionalanalys och harmonisk analys

FMA260F, 7.5 credits

Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2013-11-15

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMA260
Teaching language: English


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.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

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.

Course Literature

Renardy, M. & Rogers, Robert C.: An Introduction to Partial Differential Equations. Springer, 2004. ISBN 9780387004440.
Some further material.

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination formats: Written exam, oral exam
Grading scale: Failed, pass

Admission Details

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

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