Showing papers by "Juliette Leblond published in 2015"

Composition Operators on Generalized Hardy Spaces

Abstract: Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$ We study the composition operators $f\mapsto f\circ\phi$ on generalized Hardy spaces on $\Omega_2$, recently considered in \cite{bfl, BLRR} In particular, we provide necessary and/or sufficient conditions on $\phi$, depending on the geometry of the domains, ensuring that these operators are bounded, invertible, isometric or compact Some of our results are new even for Hardy spaces of analytic functions

Inverse skull conductivity estimation problems from EEG data

Abstract: A fundamental problem in theoretical neurosciences is the inverse problem of source localization, which aims at locating the sources of the electric activity of the functioning human brain using measurements usually acquired by non-invasive imaging techniques, such as the electroencephalography (EEG). EEG measures the effect of the electric activity of active brain regions through values of the electric potential furnished by a set of electrodes placed at the surface of the scalp and serves for clinical (location of epilepsy foci) and functional brain investigation. The inverse source localization problem in EEG is influenced by the electric conductivities of the several head tissues and mostly by the conductivity of the skull. The human skull is a bony tissue consisting of compact and spongy bone compartments, whose shape and size vary over the age and the individual’s anatomy making difficult to accurately model the skull conductivity.