This preprint was accepted October 1996.
Contact: M. I. Belishev
ABSTRACT: This is the first paper included in a planned series of articles entitled ``Boundary Control and Inverse Problems". It deals with one approach to Inverse Problems (so-called ``BC-method") based upon ideas and results of the Boundary Control Theory. One-dimensional variant of the method is demonstrated on the case of classical problem of recovering a density of inhomogeneous string. Both dynamical and spectral statements of the problem are considered. The paper is written so that to be an introduction to the multidimensional BC-method. Bibliography--23.