--All attending student please sign up on ILIAS-- (link)
Lecturer: Dr. Georgios Psaradakis (B6 - Office C4.03)
Lecture: Mo. 10:15- 11:45, and Fri. 12:00- 13:30
Tutorial: Mo. 12:00 - 13:30
Location: WIM-Zoom-6 (see Portal2 for link and password)
Prerequisites: Linear algebra I, Analysis I,II.
Requirement for Examination: obtain 50% score in average for all homework exercises.
It is a master course, however, all bachelor students who have already „Analysis I and II“ are welcome to join.
The main reference will be:
You can get them in the following SpringerLinks (internet connection provided by the Univ. Mannheim is required)
The course splits into three parts: the first one is a crash course on measure and integration, plus a version of the Riesz representation theorem. In the second part, after learning some basic facts about convex and Lipschitz functions, we will focus on the theory of Lp spaces. With the knowledge gained from the first two parts, we will learn about: the Fourier transform in L2,the symmetric-decreasing rearrangement of functions, distributions, … . Some of the inequalities to prove: Fatou, Brunn-Minkowski, isoperimetric, Hölder, Minkowski, Hanner, Hardy-Littlewood, Polya-Szegö, one dimensional Riesz rearrangement, Young, one dimensional Hardy, Hardy-Littlewood-Sobolev, Lp-Sobolev and logarithmic Sobolev. Some facts we are going to use without proof: Hahn-Banach theorem, divergence theorem, Sard’s lemma. For the first and beginning of the second parts of the course, we will use these lecture notes. The reference book for the course is: Lieb, E. H.; Loss, M. - Analysis (2nd ed.) Grad. Stud. Math. Vol. 14, Amer. Math. Soc. 2001