Canonical form of $C^*$-algebra of eikonals related to the metric graph

M. I. Belishev; A. V. Kaplun

doi:10.4213/im9179

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arXiv · 2212.05306

Canonical form of $C^*$-algebra of eikonals related to the metric graph

M. I. Belishev·A. V. Kaplun

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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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M. I. Belishev, A. V. Kaplun. 2022-12-10. Canonical form of $C^*$-algebra of eikonals related to the metric graph. https://doi.org/10.4213/im9179

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