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FSF3627 Fourier Analysis I 7.5 credits

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3627 (Spring 2019–) are denoted with an asterisk ( )

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

No information inserted

Equipment

No information inserted

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

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.

An oral examination

Other requirements for final grade

Passed oral examination.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

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

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

No information inserted

Contact

Håkan Hedenmalm (haakanh@kth.se)

Postgraduate course

Postgraduate courses at SCI/Mathematics