A $C^*$-algebra associated with dynamics on a graph of strings

Abstract

An operator $C^*$-algebra $\mathfrak E$ associated with a dynamical system on a metric graph is introduced. The system is governed by the wave equation and controlled from boundary vertices. Algebra $\mathfrak E$ is generated by eikonals, which are self-adjoint operators related with reachable sets of the system. Its structure is studied. Algebra $\mathfrak E$ is determined by the boundary inverse data. This shows promise of its possible applications to inverse problems.