Upper bounds for the many‐channel Marchenko transformation operator and its derivatives

peer reviewedWe specify the class of perturbative complex matrix potentials for which the corresponding many-channel Marchenko type transformation operators are bounded and integrable. Our reference matrix potential contains Coulomb interactions, different threshold energies, and centrifugal potentials with different angular momenta. Estimates for the transformation operator and its derivatives are obtained; they enable us to improve our recent results and are necessary for the establishment of a unique solution to the ''generalized Marchenko fundamental equation.'' From the existence of an integrable transformation operator, the analyticity of the Jost solution as a function of k1 is deduced in the upper-half of the physical k1 plane