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

抄録

An operator C^*-algebra 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 𝔈 is generated by eikonals, which are self-adjoint operators related with reachable sets of the system. Its structure is studied. Algebra 𝔈 is determined by the boundary inverse data. This shows promise of its possible applications to inverse problems.