Boundary control and inverse problems: one-dimensional variant of the BC-method

This is the first paper of the planned series under the common title “Boundary control method in inverse problems.” The aim of the series is systematic exhibition of an approach to inverse problems based upon their relations with control theory. The 1d-variant of the method is exhibited on the example of the classical problem of recovering the inhomogeneous string density, both dynamical and spectral setups of the problem being considered. The paper is written so that to serve as an introduction to the multidimansional BC-method: basic tools and constructions in use are available for the further generalization to multidimensional problems. Bibl. – 33 titles, fig. – 7.