Vorlesung: Fourieranalysis
Informationen
- ECTS-Punkte: 5
- Vorlesung
- Dozent: Prof. Dr. Brigitte Forster-Heinlein
- Zeit und Ort:
Montag 14:15 - 15:45, MI 03.10.011
- Übungen
- Übungsleitung: Dipl.Math. Stefan Held
- Zeit und Ort:
* Dienstag 14:15 - 15:45, MI 00.07.011,
* Es wird jede zweite Woche eine zweistündige Übung stattfinden.
Topics
- Fourier series.
- Short review of the classical convergence theorem of Fourier series of Hölder continuous functions.
- L^2 convergence of Fourier series of L^2 functions and isometry between L^2 and l^2.
- Regularity and Fourier decay.
- Selected applications of Fourier series, e.g denoising.
- Fourier transform.
- Definition on L^1(R^n) and basic properties (inversion formula;
- behaviour under multiplication,convolution, differentiation).
- Definition on L^2 and Plancherel's formula.
- The space of tempered distributions and Fourier calculus on distributions.
- Periodic arrays of delta functions and Poisson summation.
- Selected applications of the Fourier transform, e.g. solution of partial differential equations, Heisenberg uncertainty, X-ray crystallography, Shannon sampling and digitalization of acoustic signals, construction of wavelets.
Übungen
- Übungsblatt 1
- Übungsblatt 2
- Bilder zu Blatt 2 Aufgabe 7
- Übungsblatt 3
- Übungsblatt 4
- Übungsblatt 5
- Übungsblatt 6