Local smoothing results for the backscattering transform

Inverse Problems and Applications

25 January 14:00 - 15:00


The lecture presents results obtained by Anders Melin and the lecturer. We consider the inverse backscattering problem for the Schr\"odinger 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.