- Fourierseries
- Integral kernels
- Cesaro and Abel summability
- Convergence of Fourier series
- The isoperimetric inequality
- Weyl's equidistribution theorem
- The Fourier transform on the line
- The Poisson summation formula
- Heisenberg's uncertainty principle
- The Fourier transform in higher dimensions
- Finite Fourier analysis
- Dirichlet's theorem
FSF3627 Fourier Analysis I 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3627 (Spring 2019–)Headings with content from the Course syllabus FSF3627 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After the course, the student should have sufficient depth in the field to be able to read research articles in Fourier analysis/Harmonic analysis.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in Mathematics.
Good knowledge equivalent courses SF1626 Calculus of several variables, SF1628 Complex Analysis, SF1629 Differential equations and transform methods.
Desirable to have taken also: SF2709 Integration theory, SF2707 Functional Analysis.
Literature
E. M. Stein and R. Shakarchi, Fourier Analysis, An introduction.
Examination and completion
Grading scale
G
Examination
- TENM - Oral exam, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
An oral examination
Other requirements for final grade
Passed oral examination.
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Education cycle
Third cycle