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Coursebooks 2017-2018
Harmonic analysis
MATH-405
Lecturer(s) :
Krieger JoachimLanguage:
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.
Notes/Handbook
No.
Websites
In the programs
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Harmonic analysis - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Harmonic analysis - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Harmonic analysis - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Harmonic analysis - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Harmonic analysis - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Harmonic analysis - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
Reference week
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| 21-22 |
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- Autumn semester
- Winter sessions
- Spring semester
- Summer sessions
- Lecture in French
- Lecture in English
- Lecture in German