Open Access
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


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.


Published: July, 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1334.46058
MathSciNet: MR3376587
Digital Object Identifier: 10.2969/jmsj/06731239

Primary: 34B45 , 46Lxx‎
Secondary: 35Qxx , 35R30

Keywords: Controllability , inverse problems on graphs , metric graph , reachable sets , self-adjoint operator algebras

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 3 • July, 2015
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