Canonical form of the $C^*$-algebra of eikonals related to a metric graph
- Authors: Belishev M.I.1, Kaplun A.V.1
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Affiliations:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 86, No 4 (2022)
- Pages: 3-50
- Section: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/133872
- DOI: https://doi.org/10.4213/im9179
- ID: 133872
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Abstract
The eikonal algebra $\mathfrak E$ of a metric graph $\Omega$ is an operator $C^*$-algebra defined by the dynamical system which describes the propagationof 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 tothis form is equivalent to constructing a functional model which realizes$\mathfrak E$ as an algebra of continuous matrix-valued functions on itsspectrum $\widehat{\mathfrak{E}}$. The results are intended to be used inthe inverse problem of recovering the graph from spectral and dynamical boundary data.
About the authors
Mikhail Igorevich Belishev
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Email: belishev@pdmi.ras.ru
Doctor of physico-mathematical sciences, no status
Aleksandr Vladimirovich Kaplun
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Email: alex.v.kaplun@gmail.com
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