Unified approach to classical equations of inverse problem theory

Abstract

Abstract. The boundary control (BC) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of inverse problem theory (Gelfand–Levitan, Krein and Marchenko equations) can be derived in the framework of the BC method in a unified way. Namely, to solve each of these equations one has in fact to solve a relevant boundary control problem, whereas its solution is determined by the inverse data.