In this joint work with Carlos Kenig, Johannes Sj\"ostrand and Gunther Uhlmann, we are interested in a linearization of Calder\'on's inverse problem on the Schr\"odinger equation with partial data. The problem is equivalent to determining whether the product of harmonic functions whose traces on the boundary vanish for a large subset of the boundary, is dense in the space of integrable functions. To deal with this problem, we use techniques from analytic microlocal analysis, in particular ideas coming from the proof of Kashiwara's Watermelon theorem.
Seminar on Analysis at University of Tsukuba