A $C^*$-algebra associated with dynamics on a graph of strings

Mikhail I. BELISHEV; Naoki WADA

doi:10.2969/jmsj/06731239

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July, 2015 A $C^*$-algebra associated with dynamics on a graph of strings

Mikhail I. BELISHEV, Naoki WADA

J. Math. Soc. Japan 67(3): 1239-1274 (July, 2015). DOI: 10.2969/jmsj/06731239

Abstract

An operator $C^*$-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 eikonals, which are self-adjoint operators related with reachable sets of the system. Its structure is studied. Algebra $\mathfrak E$ is determined by the boundary inverse data. This shows promise of its possible applications to inverse problems.

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Mikhail I. BELISHEV. Naoki WADA. "A $C^*$-algebra associated with dynamics on a graph of strings." J. Math. Soc. Japan 67 (3) 1239 - 1274, July, 2015. https://doi.org/10.2969/jmsj/06731239