# SF2705 Fourier Analysis 7.5 credits

A course of Fourier series and Fourier integrals.

### Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Headings with content from the Course syllabus SF2705 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

Fourier series and integrals in one variable: Pointwise convergence, convergence in L2, summation of Fourier series and integrals. Theorems of Parseval and Plancherel.

Fourier series and integrals in several variable: Fourier analysis in higher dimensions and on discrete Abelian groups.

Fourier analysis of analytic functions: Hardy functions on the unit disk, Paley-Wiener Theorem, Hardy functions and filters.

Applications: Selection of the following. Heat equation, wave equation, isoperimetric inequality, Laplace equation on the unit disk and half-plane, Szegő’s Theorem.

### Intended learning outcomes

After the course the student should be able to

• formulate central definitions and theorems within the topic of the course,
• apply and generalize theorems and methods within the topic of the course,
• describe, analyze and formulate basic proofs within the topic of the course.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed course SF1677 Foundations of Analysis.

### Recommended prerequisites

Course corresponding to SF1691 Complex analysis recommended.

### Equipment

No information inserted

### Literature

Announced no later than 4 weeks before the start of the course on the course web page.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, 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.

Written exam. For obtaining higher grades, additionally an oral exam is required.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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 web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2705

Mathematics

Second cycle