The duality principle and inversion of Laplace–Stielties transforms

Abstract

The fundamental relation between the Laplace transform, the Stielties transform, and the generalized integral equation of refraction is revealed, and a duality principle is formulated for the solution of inverse problems of radio physics. New formulas of the Laplace-transform inversion satisfying the duality principle are obtained. There is no necessity of contour integration in a complex plane for the relations found, which considerably simplifies the reconstruction of originals and makes it possible to control systematic errors in the experimental data.