Functional Analysis for ConcepTion and Assessment of Systems
The mathematical body of knowledge shared by the team members involves functional and harmonic analysis along with related fields like approximation theory, potential theory, Schur analysis or system and circuit theory. Our approach is to couple these theoretical tools with constructive optimisation techniques, and to demonstrate the efficiency of such a combination in selected application areas. The latter mainly comprise microwave electronics, notably the synthesis and tuning of circuital communication devices, as well as inverse problems in quasi-static electromagnetics, with applications to paleomagnetism in planetary sciences and imaging issues in electro- and magneto-encephalography (EEG and MEG for short) for functional and medical neurosciences. We try to balance theoretical and applied work without sacrificing any, a transverse positioning made possible by the complementary skills within the team, ranging from mathematical analysis to algorithm design and numerical optimisation, software design as well as some knowledge in microwave electronics, brain imaging and magnetometry. In all cases, the overall objective is to produce prototypical software tools for the user, dedicated to the application at hand.