Dr. Georgios Psaradakis

Dr. Georgios Psaradakis

University of Mannheim
School of Business Informatics and Mathematics
B6, 28 – Room C 4.03
68159 Mannheim


  • Fall 2020 Advanced Analysis 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

 Brief lecture notes on measure theory for the Advanced Analysis course.