Advanced analysis

Dr. Georgios Psaradakis

Mo. 12:00 - 13:30 in  A5,6 C 115

Fr.   08:30 - 10:00 in  A5,6 C 015

Tutorial:  Fr. 10:15 - 11:45 in B6,  A 101 

Content: This course will start with basic knowledge of real analysis, includes measure and integration, then we will go into some advanced topics in analysis, such as L^p spaces, symmetric decreasing rearrangement of functions and Riesz's rearrangement inequality, the Hardy-Littlewood-Sobolev inequality, the Fourier transform, distributions, Sobolev inequalities and the isoperimetric inequality. These are necessary knowledge in modern PDE theories and their applications (for example, in physics, biology and economy).

Language: English.

Prerequisites: Linear algebra I, Analysis I,II.

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:

Lieb, E. H.; Loss, M. Analysis. 2nd edition. Graduate Studies in Mathematics 14. American Mathematical Society 2001. xxii+346 pp. ISBN: 0-8218-2783-9

but for measure theory we will follow the presentation in the first chapter of

Evans, L. C.; Gariepy, R. F. Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC Press 1992. viii+268 pp. ISBN: 0-8493-7157-0

Course calendar

Homework assignments