论文标题
部分可观测时空混沌系统的无模型预测
Functional-differential operators on geometrical graphs with global delay and inverse spectral problems
论文作者
论文摘要
我们建议在涉及{\ it全局}延迟参数的几何图表上具有恒定延迟的功能分化运算符的新概念。图形上的差异操作员在许多科学技术领域的各个过程中建模了各个过程。尽管朝这个方向的绝大多数研究涉及图形上的纯差分运算符（通常称为量子图），但最近在星形图上也出现了非局部运算符的一些考虑因素。特别是，属于函数差异的运算符，具有恒定延迟，但在{\ it locally}的非局部版本中。后者意味着图的每个边缘都有其自身的延迟参数，这不会影响任何其他边缘。在本文中，我们介绍了{\ it在全球范围内}非局部运算符，这些非局部运算符预计在图形上对非局部过程进行建模更为自然。我们还将这个想法扩展到任意树，这开辟了广泛的进一步研究。本文的另一个目标是通过解决一个唯一性，频谱数据的表征以及统一稳定性的广泛问题，研究具有全球延迟的操作员的逆频谱问题。
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and technology. Although a vast majority of studies in this direction concern purely differential operators on graphs (often referred to as quantum graphs), recently there also appeared some considerations of nonlocal operators on star-type graphs. In particular, there belong functional-differential operators with constant delays but in a {\it locally} nonlocal version. The latter means that each edge of the graph has its own delay parameter, which does not affect any other edge. In this paper, we introduce {\it globally} nonlocal operators that are expected to be more natural for modelling nonlocal processes on graphs. We also extend this idea to arbitrary trees, which opens a wide area of further research. Another goal of the paper is to study inverse spectral problems for operators with global delay in one illustrative case by addressing a wide range of questions including uniqueness, characterization of the spectral data as well as the uniform stability.
