  With a densely defined symmetric semi-bounded operator of nonzero defect
indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a
topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the
reachable sets of a dynamical system governed by the equation
$u_{tt}+(L_0)^*u=0$. Wave spectra of unitary equivalent operators are
homeomorphic.
  In inverse problems, one needs to recover a Riemannian manifold $\Omega$ via
dynamical or spectral boundary data. We show that for a generic class of
manifolds, $\Omega$ is isometric to the wave spectrum $\Omega_{L_0}$ of the
minimal Laplacian $L_0=-\Delta|_{C^\infty_0(\Omega\backslash \partial \Omega)}$
acting in ${\cal H}=L_2(\Omega)$, whereas $L_0$ is determined by the inverse
data up to unitary equivalence. Hence, the manifold can be recovered (up to
isometry) by the scheme `data $\Rightarrow L_0 \Rightarrow \Omega_{L_0}
\overset{\rm isom}= \Omega$'.
  The wave spectrum is relevant to a wide class of dynamical systems, which
describe the finite speed wave propagation processes. The paper elucidates the
operator background of the boundary control method (Belishev`1986), which is an
approach to inverse problems based on their relations to control theory.
