We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = ( 0 , ∞ ) × Y whose rotation radius is constant outside some compact interval. The unitarily equivalent to direct sum of one-dimensional Schrödinger operators with compactly supported potentials half-line. prove Asymptotics counting function resonances at large radius. uniquely determined by its e...

We address the inverse problem for scattering of acoustic waves due to an inhomogeneous medium. We derive and analyze the Hessian in both Hölder and Sobolev spaces. Using an integral equation approach based on Newton potential theory and compact embeddings in Hölder and Sobolev spaces, we show that the Hessian can be decomposed into two components, both of which are shown to be compact operator...