Teaching

Type:	Time:	Place:	Start:
Lecture (VO) 3 hrs.	Mon 9:45-11:15 (every other week) Mi 13:15-14:45	SR11 SR07	2.3.
Proseminar (PS) 1 hrs.	Mon 9:45-11:15 (every other week)	PC-SR3	9.3.

The following problems are to be solved [PDF]:

• 9.3: 1-8
• 23.3: 9-16
• 20.4: 17-24
• 4.5: 25-32
• 18.5: 32-40
• 1.6: 41-48
• 15.6: 49-56
• 29.6: 57-64

L^p spaces (convolution, approximation, Lebesgue points, characterization of absolutely continuous functions), Fourier analysis. I am following my notes and the content is:

• 1. Recap measure theory
• 2. Integration (except 2.5 and 2.6))
• 3. Lebesgue spaces (except 3.6)
• 4. More measure theory
• 6. The dual of L^p
• 9. The Fourier transform (except 9.5 and 9.6)
• 10. Interpolation and Applications (except 10.3)

Module Electives in the Master's programme in Mathematics.

The course assessment for the lecture will be via an oral examination at the end of the course. The course assessment for the exercises will be via presenting solutions during class. The checkmarks will only count if you are present and contribute 25% to the final grade (the lowest result will be dropped). The number of presentations will contribute 75% to the final grade.

Some textbooks:

1. E. Lieb and M. Loss, Analysis, 2nd ed., GSM 14, AMS, Providence, 2001
2. W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, Boston 1987.
3. E. M. Stein und R. Shakarchi, Fourier Analysis, Princeton UP, Princeton, 2003.
4. E. M. Stein und R. Shakarchi, Real Analysis, Princeton UP, Princeton, 2005.
5. G. Teschl, Topics in Real Analysis, lecture notes.