Teaching

Type:	Time:	Place:	Start:
Lecture (VO) 2 hrs.	Tue 9:45-11:15	HS2	5.3.

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

• Recap measure theory (Sections 1.1-1.5)
• Recap integration theory (Sections 2.1-2.3)
• Lebesgue spaces (Sections 3.1-3.5)
• More measure theory (Sections 4.1-4.3; last section without proo)
• The dual of L^p (Sections 6.1-6.3; last section without proofs)
• The Fourier transform (8.1,8.3)
• Interpolation (9.1-9.2)

Module "Advanced Functional Analysis" 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.

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.