Multipoint formulas for inverse scattering at high energies

International audienceWe consider inverse scattering for the multidimensional Schrödinger equation with smooth compactly supported potential v.We give explicit asymptotic formulas for the Fourier transform Fv(p) at fixed p in terms of the scattering amplitude fat n points at high energies. The precision of these formulas is proportional to n.To our knowledge these formulas are new for n≥ 2, whereas they reduce to the Born formula at high energies for n=1