Harmonic Analysis (Summer Semester 2021)
- Lecturer: Prof. Dr. Dorothee Frey
- Classes: Lecture (0156400), Problem class (0156410)
- Weekly hours: 4+2
The course will be held online (at least at the beginning).
All relevant course information can be found on the study platform Ilias.
|Lecture:||Monday 10:00-23:59||20.30 SR 3.61||Begin: 12.4.2021|
|Wednesday 8:00-23:59||20.30 SR 3.68|
|Problem class:||Friday 10:00-11:30||20.30 - 01.25||Begin: 16.4.2021|
|Lecturer||Prof. Dr. Dorothee Frey|
|Office hours: Tuesday, 10am - 11am, and by appointment|
|Room 2.042 Kollegiengebäude Mathematik (20.30)|
|Email: firstname.lastname@example.org||Problem classes||Dr. Nick Lindemulder|
|Room 2.044 Kollegiengebäude Mathematik (20.30)|
This course gives an introduction to Fourier analysis and real harmonic analysis. Harmonic analysis has its origin in Fourier's work, which provides explicit solutions for e.g. heat and wave equations. Nowadays, it provides important tools in tackling a large variety of problems coming from partial differential equation, in particular for boundary value problems on spaces. Topics of the course include summability of Fourier series, the Fourier transform on , interpolation methods, singular integral operators, and Fourier multipliers.
- Fourier series
- Fourier transform on and
- Tempered distributions and Fourier transforms
- Explicit solutions of heat equation, wave equation and Schrödinger equation on
- Hilbert transform
- Interpolation theorem of Marcinkiewicz
- Singular integral operators
- Mihlin multiplier theorem
Basic knowledge in Functional Analysis is recommended.
Oral exam of approx. 30 minutes.
- Y. Katznelson. An introduction to harmonic analysis. Third edition. Cambridge University Press, Cambridge, 2004.
- L. Grafakos. Classical Fourier analysis. Third edition. Graduate Texts in Mathematics, 249. Springer, New York, 2014.
- E. M. Stein. Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970
- E. M. Stein; R. Shakarchi. Fourier analysis. An introduction. Princeton Lectures in Analysis, 1. Princeton University Press, Princeton, NJ, 2003.