# Coursebooks

## Harmonic analysis

Krieger Joachim

English

#### Summary

An introduction to methods of harmonic analysis. Covers convergence of Fourier series, Hilbert transform, Calderon-Zygmund theory, Fourier restriction, and applications to PDE.

#### Content

-Fourier series, convergence and summability.

-Fourier series, convergence and summability.

-Hilbert transform.

-Calderon-Zygmund theory of singular integrals.

-Liitlewood-Paley theory.

-Fourier restriction.

-Applications to dispersive PDE.

#### Keywords

Fourier series, convergence, singular integrals, Calderon-Zygmund theory, Fourier restriction.

#### Learning Prerequisites

##### Required courses

Analyse I - IV, Algebre lineaire I et II.

##### Recommended courses

Analyse I - IV, Algebre lineaire I et II.

##### Important concepts to start the course

Understand key concepts of real analysis, such as measure and Lebesgue integral. Be able to construct a rigorous mathematical argument.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Analyze convergence of Fourier series
• Examine bounds for singular integrals
• Prove bounds for dispersive PDE

#### Transversal skills

• Communicate effectively with professionals from other disciplines.
• Access and evaluate appropriate sources of information.
• Give feedback (critique) in an appropriate fashion.

#### Teaching methods

Two hours ex cathedra lectures, two hours of exercises led by teaching assistant.

#### Expected student activities

Attend lectures and exercise sessions, read course materials, solve exercises.

#### Assessment methods

Oral exam at the end of course.

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

#### Supervision

 Office hours No Assistants Yes Forum No

#### Resources

##### Bibliography

-Classical multilinear harmonic analysis by C. Muscalu and W. Schlag.

-Singular integrals and differentiability properties of functions by E. Stein.

No.

### In the programs

• Applied Mathematics, 2018-2019, Master semester 2
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Harmonic analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2018-2019, Master semester 4
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Harmonic analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 2
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Harmonic analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 2
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Harmonic analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 4
• Semester
Spring
• Exam form
Oral
• Credits
5
• Subject examined
Harmonic analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

MoTuWeThFr
8-9
9-10MAA331
10-11
11-12
12-13
13-14MAA331
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German