Stability of the solution to 3D fixed-energy inverse scattering problem

AbstractLet supα′,α ϵ S2 ¦Aδ(α′, α) − A(α′, α)¦ < δ, where S2 is the unit sphere in R3, A(α′, α) is the unknown scattering amplitude corresponding to a potential q(x) ϵ Qa: = {q: q = q̄, q ϵ L2(Ba), q = 0 in B′a}, Ba: = {x: ¦x¦⩽ a, x ϵ R3}, a > 0 is a given number, B′a = R3βBa, δ > 0 is a small number. A numerical method is given to calculate a stable approximation q̂δ to the Fourier transform q̃(λ) of q(x). An estimate of the error of the approximation is given for q ϵ Qq and q ϵ Qa ∩ L∞(Ba)