  We consider inverse problems for wave, heat and Schr\"odinger-type operators
and corresponding spectral problems on domains of ${\bf R}^n$ and compact
manifolds. Also, we study inverse problems where coefficients of partial
differential operator have to be found when one knows how much energy it is
required to force the solution to have given boundary values, i.e., one knows
how much energy is needed to make given measurements. The main result of the
paper is to show that all these problems are shown to be equivalent.
