论文标题
$ c^*$ - 艾科纳群岛代数的规范形式与公制图
Canonical form of $C^*$-algebra of eikonals related to the metric graph
论文作者
论文摘要
公制图$ω$的eikonal代数$ \ Mathfrak e $是运算符$ c^*$ - 由动态系统定义的代数，它描述了由$ω$的边界顶点支持的源产生的波的传播。本文介绍了任意紧凑型公制图的代数$ \ mathfrak e $的规范块形式。传递此形式等同于构建功能模型，该功能模型将$ \ mathfrak e $视为其频谱上连续矩阵值函数的代数，其频谱$ \ wideHat {\ mathfrak {\ mathfrak {e}} $。结果旨在通过光谱和动态边界数据在图形重建的反面问题中使用。 参考书目：28个项目。
The eikonal algebra $\mathfrak E$ of the metric graph $Ω$ is an operator $C^*$--algebra defined by the dynamical system which describes the propagation of waves generated by sources supported in the boundary vertices of $Ω$. This paper describes the canonical block form of the algebra $\mathfrak E$ of an arbitrary compact connected metric graph. Passing to this form is equivalent to constructing a functional model which realizes $\mathfrak E$ as an algebra of continuous matrix-valued functions on its spectrum $\widehat{\mathfrak{E}}$. The results are intended to be used in the inverse problem of reconstruction of the graph by spectral and dynamical boundary data. Bibliography: 28 items.
