BOUNDARY CONTROL AND A MATRIX INVERSE PROBLEM FOR THE EQUATION U(TT)-U(XX)+V(X)U=O

The authors solve the problem of recovering the matrix-valued potential V(x) , x > 0, from the given reaction operator R: u(0, t) bar arrow pointing right u(x)(0, t) , t > 0. They show the connections between this problem and the theory of boundary control. which allows them to obtain analogues of the classical Gel'fand-Levitan-Krein equations. They establish the basis property for a family of vector-valued exponentials; this property is connected with the spectral characteristics of the boundary value problem. They prove the controllability of the corresponding system under a boundary control u(0, t) = f(t).