正则图和半正则图的径向邻接
Radial Averages on Regular and Semiregular Graphs
摘要：
1966年，P. Günther证明了以下结果：给定常曲率紧致曲面$M$上的连续函数$f$及其到泛覆盖（双曲平面）的周期提升$\tilde{f}$，则提升$\tilde{f}$在增加球面上的平均值收敛于函数$f$在曲面$M$上的平均值。在这篇文章中，我们证明了类似的结果，对函数的顶点和边的正则和半正则图，特别强调的收敛速度。然而，我们考虑更一般的集合，即球面弧的平均值，这反过来又意味着管和horocycles以及领域的结果。
英文摘要：
In 1966, P. Günther proved the following result: Given a continuous function $f$ on a compact surface $M$ of constant curvature -1 and its periodic lift $\tilde{f}$ to the universal covering, the hyperbolic plane, then the averages of the lift $\tilde{f}$ over increasing spheres converge to the average of the function $f$ over the surface $M$. In this article, we prove similar results for functions on the vertices and edges of regular and semiregular graphs, with special emphasis on the convergence rate. However, we consider averages over more general sets, namely spherical arcs, which in turn imply results for tubes and horocycles as well as spheres.
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