Canonical form of $C^{\ast }$-algebra of eikonals related to the metric graph

Abstract

The eikonal algebra $\mathfrak{E}$ of the metric graph $\Omega$ is an operator $C^{\ast }$--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 $\hat{\mathfrak{E}}$. 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.

References in corpus (2)

• On an inverse problem for tree-like networks of elastic strings
• Eikonal algebra on a graph of simple structure