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.

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.