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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Eikonal algebra on a graph of simple structure
M. I. Belishevab, A. V. Kaplunb a Saint-Petersburg Department of the Steklov Mathematical Institute, RAS,
27 Fontanka, St Petersburg 191023, Russia
b Saint-Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia
Аннотация:
An eikonal algebra $\mathfrak{E}(\Omega)$ is a $C^*$-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are initiated by boundary sources (controls) and propagate into the graph with finite velocity. Motivation and interest to eikonal algebras comes from the inverse problem of reconstruction of the graph via its dynamical and/or spectral boundary data. Algebra $\mathfrak{E}(\Omega)$ is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of $\Omega$. We demonstrate such connections and study $\mathfrak{E}(\Omega)$ by the example of $\Omega$ of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.
Ключевые слова:
metric graph, hyperbolic dynamical system, reachable sets, $C^*$-algebra of eikonals.
Поступила в редакцию: 01.03.2018 Принята в печать: 02.07.2018
Образец цитирования:
M. I. Belishev, A. V. Kaplun, “Eikonal algebra on a graph of simple structure”, Eurasian Journal of Mathematical and Computer Applications, 6:3 (2018), 4–33
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ejmca118 https://www.mathnet.ru/rus/ejmca/v6/i3/p4
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Страница аннотации: | 88 | PDF полного текста: | 33 |
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