Warning! The directory is not yet complete and will be amended until the beginning of the term.

250081 VO Real analysis (2023S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Karlheinz Gröchenig

Classes (iCal) - next class is marked with N

This (mandatory) course usally counts two hours per semester. This time it will take place during the first half of the semester until the end of April with four hours per semester. It may serve as a preparation for the special topics course that is to follow in May and June.

Wednesday 01.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 03.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday 08.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 10.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday 15.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 17.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday 22.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 24.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday 29.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 31.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday 19.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 21.04. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday 26.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday 28.04. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

1. Most general form of the fundamental theorem of calculus
Maximal function, its boundedness, Lebesgue differentiation theorem,
2. Approximation with convolution kernels, L^p-convergence, pointwise convergence
3. Absolute continuity and differentiation
4. Some Fourier analysis
5. Sobolev spaces, Fourier analytic approach

Prerequisites: Lebesgue integration, convergence theorems, L^p-spaces (from third semester bachelor course)

Assessment and permitted materials

Oral exam at the end of the course.

Minimum requirements and assessment criteria

Detailed knowledge of course material and its applications. To pass, at least half of the questions need to be answered correctly.
Theoretical list of grades:
88-100 sehr gut
75-87 gut
62-74 befriedigend
50-61 genuegend
<50 nicht genuegend

Examination topics

Entire course material.

Reading list

A.~ Constantin, "Fourier analysis. Part I. Theory." (from Chs. 2,4,5)
E.~Hewitt, K.~ Stromberg, Real and abstract analysis. Springer
B.~Simon, Harmonic analysis. A Comprehensive Course in Analysis, Part 3. AMS.
E.~Lieb, M.~Loss, Analysis, AMS, 2001.
E. M. Stein und R. Shakarchi, Fourier Analysis, Princeton UP, Princeton, 2003.
E. M. Stein und R. Shakarchi, Real Analysis, Princeton UP, Princeton, 2005.
G.~ Teschl, Topics in Real and Functional Analysis, (Chs.~8-12), lecture notes
available on Teschl's homepage.

Association in the course directory

MANF

Last modified: Mo 12.02.2024 10:06