Canonical form of \(C^\)-algebra of eikonals related to the metric graph

The eikonal algebra \(\mathfrak E\) of the metric graph \(\Omega\) is an operator \(C^*\)--algebra defined by the dynamical system which describes the propagation of waves generated by sources supported in the boundary vertices of \(\Omega\). This paper describes the canonical block form of the algebra \(\mathfrak E\) of an arbitrary compact connected metric graph. Passing to this form is equivalent to constructing a functional model which realizes \(\mathfrak E\) as an algebra of continuous matrix-valued functions on its spectrum \(\widehat{\mathfrak{E}}\). The results are intended to be used in the inverse problem of reconstruction of the graph by spectral and dynamical boundary data. Bibliography: 28 items.