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Fourieranalysis/ Fourier Analysis Semester
WiSe 2017 / 18
Lecturer
Helmut Abels
Type of course (Veranstaltungsart)
Vorlesung
Contents
We give an introduction to the theory of Fourier series of periodic functions and the Fourier transformation for function on the Euclidean space R^n. We plan to address the following subjects:
- Convergence of Fourier series and the Gibbs phenomenon
- Plancherel's theorem (Fourier transformation is an isomorphism on L^2)
- application to partial differential equations using a separation of variables
- smoothness of functions and the decay behaviour of its Fourier transform
- Schwarz functions, tempered distributions and applications to function spaces (in particular Sobolev spaces).
- Translation invariant and singular integral operator
Literature
- H. Abels: Pseudodifferential and Singular Integral Operators, de Gruyter, 2012
- J. Duoandikoetxea, Fourier Analysis, AMS Publication, 2001
- Y. Katznelson: An Introduction to Harmonic Analysis, Cambridge Mathematical Library, 2004
Recommended previous knowledge
Basic knowledge in the calculus in multiple variables, integration and measure theory (Lebesgue integral) as taught in Analysis I-III in Regensburg.
Time/Date
Tuesday, 14-16
Location
M103
Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=29936
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)
Registration- Preliminary registration for the organisation of exercise classes: at the end of the previous
semester via EXA or LSF (see announcement by the department) - Registration for the exercise classes: During the first week of the lecture time via GRIPS
- Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)- Successful participation in the exercise classes: 50% of the maximal points in the
exercise
sheets, presentation of one solution
Examination (Prüfungsleistungen)- Oral exam: Duration: 20 minutes, Date: individual, by appointment, re-exam: Date: individual,
by appointment - Combined exam in agreement with the lecturer in combination with, e.g.: Evolution Equations I
(in summer term 2018), oral exam: Duration: 30 minutes, Date: individual, by appointment
Regelungen bei Studienbeginn vor WS 2015 / 16- Benotet:
- O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
- Unbenotet:
- O. g. Studienleistung und Bestehen der o. g. Prüfungsleistung
Additional comments
The exercise classes will be biweekly.
(2 hours lecture series, 1 hour exercise classes)
Modules
BV, MV, MAngAn, PHY-B-WE3, PHY-M-VE3, CS-B-Math4, CS-M-P1, CS-M-P2, CS-M-P3
ECTS
4.5
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