Ingrid Beltita: Local smoothing results for the backscattering transform

The lecture presents results obtained by Anders Melin and the lecturer. We consider the inverse backscattering problem for the Schrödinger operator in odd dimensions. The backscattering transform of the potential v is, up to a smooth function, the real part of the inverse Fourier transform of the backscattering part of the scattering matrix. We shall show that this mapping is entire analytic in v, between appropriate spaces, and give local smoothing properties for each term in the power series expansion at 0.