Geodesic
Canonical form of the $C^*$-algebra of eikonals related to a~metric graph
Izvestiya. Mathematics , Tome 86 (2022) no. 4, pp. 621-666

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The eikonal algebra $\mathfrak E$ of a metric graph $\Omega$ is an operator $C^*$-algebra defined by the dynamical system which describes the propagation of waves generated by sources supported at the boundary vertices of $\Omega$. This paper describes the canonical block form of the algebra $\mathfrak E$ for 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 recovering the graph from spectral and dynamical boundary data.
Keywords: dynamical system on a metric graph, reachable sets, eikonal $C^*$-algebra, canonical form. 
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     title = {Canonical form of the  $C^*$-algebra of eikonals related to a~metric graph},
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M. I. Belishev; A. V. Kaplun. Canonical form of the  $C^*$-algebra of eikonals related to a~metric graph. Izvestiya. Mathematics , Tome 86 (2022) no. 4, pp. 621-666. http://geodesic.mathdoc.fr/item/IM2_2022_86_4_a0/