250044 VO Fourier Methods on Manifolds with Applications (2019W)
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Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Thursday 03.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 10.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 17.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 24.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 31.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 07.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 14.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 21.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 28.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 05.12. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 12.12. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 09.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 16.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 23.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 30.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Fourier methods have been proven very powerful in many areas of pure and applied mathematics. In particular, the Fast Fourier Transform (FFT) builds a very effective bridge between the rich field of Fourier analysis and numerical implementations. Applications embrace for instance signal/image processing, tomographic reconstruction, solving of partial differential equations, simulation of dynamical systems.The goal of the course is to provide an insight in the range of applications where Fourier methods are particular fruitful. The first part pays attention to classical Fourier analysis of periodic functions (on the circle). After recalling some fundamentals of Fourier series and function spaces, we shall get a first glimpse how Fourier methods can efficiently solve selected problems. Afterwards we like to generalize the concepts to Riemannian manifolds, including examples of recent research.Depending on the knowledge or preference of the audience, we may focus on specific topics from harmonic analysis, geometry, optimization or numerical implementation.
Assessment and permitted materials
Oral examination.
Minimum requirements and assessment criteria
Minimum requirements:
Knowledge in advanced analysis (Bachelors degree) with interests in numerical mathematics should be sufficient. Basic understanding in Fourier analysis, Hilbert space theory and differential geometry is advantageous.
Knowledge in advanced analysis (Bachelors degree) with interests in numerical mathematics should be sufficient. Basic understanding in Fourier analysis, Hilbert space theory and differential geometry is advantageous.
Examination topics
The material presented in the lecture.
Reading list
Introductory text books to Fourier analysis:
Folland: Fourier Analysis and Its Applications
Gasquet, Witomski: Fourier Analysis and Applications
Folland: Fourier Analysis and Its Applications
Gasquet, Witomski: Fourier Analysis and Applications
Association in the course directory
MGEV, MANV, MAMV
Last modified: We 21.04.2021 00:21