The purpose of the School is to introduce young African mathematicians to some recent developments of Real and complex Analysis, as well as to its role in Applications of Mathematics. On one side we will focalize on properties of spaces of holomorphic functions and operators acting on them, on another side we will develop their links with applications, in particular with controllability of linear systems and inverse problems in potential theory (that arise for instance in medical engineering). Complex analysis will also be considered in relation with sampling and uncertainty in signal processing, and numerical aspects will be developed for a remarkable system of orthogonal functions due to Slepian and Pollack.
The School will be the occasion to present spectacular new results on the corona problem, whose solution in dimension one is due to Carleson in the sixties and generalization to the unit ball in higher dimension is still open.
We will insist on the interplay between theoretical aspects and applications. We feel that it is particularly important for young researchers in analysis to understand the necessity of a solid theoretical background as well as the importance of real life applications.
Buea University is an English speaking university in Cameroon. So it is particularly adapted to build a bridge between the Anglophone and Francophone Mathematical communities in West and Central Africa. The language of the organized activities of the CIMPA school will be English.
There is a group of young analysts in Cameroon (and among them two in Buea), who will be particularly involved in this CIMPA school. This will help them to train a new generation of analysts during the next years. It will also be the occasion for participants to see how techniques of analysis are involved in many aspects of applications of mathematics. Moreover, this CIMPA school will answer a real need for training in analysis for young or less young teachers at the universities of the region. Some have been trained in analysis for their PhD thesis, but are isolated since then. The CIMPA school will be the occasion of international contacts, which is always very fruitful. It has been planned to benefit from the effective international cooperation between lecturers.