Title: Geometrical optics solutions for nonlocal scattering
Abstract: We will discuss the construction of geometrical optics solutions for Helmholtz-type equations of nonlocal nature. In particular, we will consider the case of the fractional Laplacian with variable refraction index and potential. Our approach consists of first constructing approximate geometrical optics solutions via a stationary - non-stationary phase argument and then upgrading these to exact solutions via a positive commutator argument. We will also show an application of these results to the study of the corresponding nonlocal inverse problem. The talk is based on a joint work with Professors Maarten de Hoop and Mikko Salo.
