论文标题
简单结构图上的Eikonal代数
Eikonal algebra on a graph of simple structure
论文作者
论文摘要
Eikonal代数$ {\ Mathfrak E}（ω）$是与公制图$ω$相关的C*-Algebra。它是由与图形相关的动力系统的轨迹和可及的集合确定的。该系统描述了由边界源（控件）启动的波，并以有限的速度传播到图中。 Eikonal代数的动机和兴趣来自图形通过其动力学和/或光谱边界数据重建的反面问题。代数$ {\ mathfrak e}（ω）$由这些数据确定。同时，其结构和代数不变式（不可约表示）与$ω$相连。我们以简单结构的$ω$的示例来证明这种连接并研究$ {\ mathfrak e}（ω）$。希望将来，这些联系将提供重建方法。
An eikonal algebra ${\mathfrak E}(Ω)$ is a C*-algebra related to a metric graph $Ω$. 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 ${\mathfrak E}(Ω)$ is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of $Ω$. We demonstrate such connections and study ${\mathfrak E}(Ω)$ by the example of $Ω$ of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.
