A C*-algebra associated with dynamics on a graph of strings
| Autor: | Belishev, M. I., Wada, N. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A C*-algebra $\mathfrak E$ associated with a dynamical system on a metric graph is introduced. The system is governed by the wave equation and controlled from boundary vertices. Algebra $\mathfrak E$ is generated by the so-called {\it eikonals}, which are self-adjoint operators related with reachable sets of the system. Its structure is the main subject of the paper. We show that $\mathfrak E$ is a direct sum of "elementary blocks". Each block is an algebra of operators multiplying ${\mathbb R}^n$-valued functions by continuous matrix-valued functions of special kind. The eikonal algebra is determined by the boundary inverse data. This shows promise of its possible applications to inverse problems. |
| Databáze: | arXiv |
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