Ramm, Alexander G.Ramm, A. G.Shivakumar, P. N.Strauss, A. V.2012-07-252012-07-252000http://hdl.handle.net/2097/14089A detailed discussion of the Krein’s results (applicable for solving the inverse scattering problem) is given with complete proofs. It is shown that the S-function S(k) used in Krein’s work is the S-matrix used in physics. The basic new results of the paper include the detailed description and analysis of an inversion algorithm based on Krein’s results and a proof of its consistency, that is the proof that the reconstructed potential generates the same scattering data from which it was reconstructed. Numerical advantages of using Krein’s method are discussed.This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).Krein's methodInverse scatteringInversion algorithmBook chapter (author version)