FSF3627 Fourier Analysis I 7.5 credits
Content and learning outcomes
Course contents
- 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
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.
Recommended prerequisites
Equipment
Literature
E. M. Stein and R. Shakarchi, Fourier Analysis, An introduction.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
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.
An oral examination
Other requirements for final grade
Passed oral examination.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed 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.