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250062 VO Real analysis (2016S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Friday 04.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 18.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 08.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 15.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 22.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 29.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 06.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 13.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 20.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 27.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 03.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 10.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 17.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 24.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The following topics will be presented:

- basic measure theory
- Lebesgue measure and integration (convergence theorems, Fubini’s theorem,
transformation theorem, etc.)
- L^p spaces (convolution and approximation, dual spaces, interpolation theorems, etc.)
- complex measures, Radon-Nikodym theorem, Lebesgue decomposition
- differentiation and integration (Hardy-Littlewood maximal function, Lebesgue
differentiation theorem, absolutely continuous funkcions, Rademacher’s theorem, etc.)
- Fourier analysis (Fourier transform, Lemma of Riemann-Lebesgue, Fourier
inversion theorem, Plancherel’s theorem, Paley-Wiener theorems, etc.)

Assessment and permitted materials

Oral examination

Minimum requirements and assessment criteria

Positive examination

Examination topics

Those parts of the provided lecture notes presented in the course

Reading list

Lecture notes will be provided. Further reading:

- G. B. Folland, Real analysis, second ed., Pure and Applied Mathematics (New York),
John Wiley & Sons Inc., New York, 1999.

- L. Grafakos, Classical Fourier analysis, second ed., Graduate Texts in Mathematics,
vol. 249, Springer, New York, 2008.

- Y. Katznelson, An introduction to harmonic analysis, third ed.,
Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2004.

- E. H. Lieb and M. Loss, Analysis, second ed., Graduate Studies in Mathematics,
vol. 14, American Mathematical Society, Providence, RI, 2001.

- W. Rudin, Real and complex analysis, third ed., McGraw-Hill Book Co., New York, 1987.

- E. M. Stein and R. Shakarchi, Real analysis, Princeton Lectures in Analysis, III,
Princeton University Press, Princeton, NJ, 2005.

Association in the course directory

MANF

Last modified: Mo 07.09.2020 15:40