论文标题
公制图的规范形式的eikonal代数和图几何形式
Canonical forms of metric graph eikonal algebra and graph geometry
论文作者
论文摘要
eikonals $ \ mathfrak e $的代数$ω$是运算符$ c^*$ - 由动态系统确定的，用边界控制来描述图表上的波传播。在本文中，为任意连接的本地紧凑型图提供了代数$ \ mathfrak e $的两个规范块形式（代数和几何）。这些表格确定一些度量图（帧）$ \ Mathfrak f^{\，\ rm a} $和$ \ Mathfrak f^{\，\ rm g} $。框架$ \ mathfrak f^{\，\ rm a} $由边界逆数据确定。框架$ \ mathfrak f^{\，\ rm g} $与图几何相关。引入了一类普通图，它们的帧相同：$ \ Mathfrak f^{\，\ rm a} \ equiv \ equiv \ mathfrak f^{\，\ rm g} $。结果应在反问题中使用，该问题包括从其边界反向数据确定图。
The algebra of eikonals $\mathfrak E$ of a metric graph $Ω$ is an operator $C^*$-algebra determined by dynamical system with boundary control that describes wave propagation on the graph. In this paper, two canonical block forms (algebraic and geometric) of the algebra $\mathfrak E$ are provided for an arbitrary connected locally compact graph. These forms determine some metric graphs (frames) $\mathfrak F^{\,\rm a}$ and $\mathfrak F^{\,\rm g}$. Frame $\mathfrak F^{\,\rm a}$ is determined by the boundary inverse data. Frame $\mathfrak F^{\,\rm g}$ is related to graph geometry. A class of ordinary graphs is introduced, whose frames are identical: $\mathfrak F^{\,\rm a}\equiv\mathfrak F^{\,\rm g}$. The results are supposed to be used in the inverse problem that consists in determination of the graph from its boundary inverse data.
