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Canonical form of $C^*$-algebra of eikonals related to the metric graph (2212.05306v1)

Published 10 Dec 2022 in math.OA, math-ph, and math.MP

Abstract: 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.

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