图序列的收敛定理
Convergence theorems for graph sequences
摘要：
本文讨论了定义在点度一致有界的有限图集合上的巴拿赫空间值映射的概念。这些函数将被赋予一定的有界性和可加性准则。我们沿着一类特定的图序列检查它们的规范化长期行为。利用Elek提出的方法，证明了当相应的图序列具有超有限结构时，在巴拿赫空间的拓扑中收敛.这些考虑扩展和补充了相应的结果顺从的群体。作为应用，我们验证了离散结构上有界有限值域算子积分态密度的一致逼近。此外，我们扩展的结果有关的抽象版本的Fekete引理顺从的群体和可取消半群的几何情况下收敛的图形序列。
英文摘要：
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We examine their normalized long-term behaviour along a particular class of graph sequences. Using techniques developed by Elek, we show convergence in the topology of the Banach space if the corresponding graph sequence possesses a hyperfinite structure. These considerations extend and complement the corresponding results for amenable groups. As an application, we verify the uniform approximation of the integrated density of states for bounded, finite range operators on discrete structures. Further, we extend results concerning an abstract version of Fekete's Lemma for amenable groups and cancellative semigroups to the geometric situation of convergent graph sequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
