S -matrix inverse scattering problem via the fixed-point theorem
James T. Cushing · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1978
By use of the contraction mapping principle we show explicitly that the equations for the inverse scattering problem [i.e., constructing the full amplitude, $A (s,t)$, from just the $s$-wave amplitude ${A}_{0}(s)$ given at all real $s$ in nonrelativisitic $S$-matrix theory have a locally unique solution when there are no pole terms and no subtractions and when the relevant norms are sufficiently small. The corresponding mapping problem for the relativistic, crossing-symmetric case is also formulated and the question of uniqueness is discussed.