AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0},
{x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with
zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix
{\partial_{t}a} is known.
A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem