arXiv subjects

Femke Douma

Publications and source records attributed to Femke Douma.

3 recordsLinked to original sources

arXiv2010

A Lattice Point Problem on the Regular Tree

Heinz Huber (1956) considered the following problem on the the hyperbolic plane H. Consider a strictly hyperbolic subgroup of automorphisms on H with compact quotient, and choose a conjugacy class in this group. Count the number of vertices inside an increasing ball, which are images of a fixed point x in H under automorphisms in the chosen conjugacy class, and describe the asymptotic behaviour of this number as the size of the ball goes to infinity. We use a well-known analogy between the hyperbolic plane and the regular tree to solve this problem on the regular tree.

math.CO↗

arXiv2009

Radial Averages on Regular and Semiregular Graphs

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.

math.CO↗

arXiv2008

Spherical Averages on Regular and Semiregular Graphs

In 1966, P. Guenther proved the following result: Given a continuous function f on a compact surface M of constant curvature -1 and its periodic lift g to the universal covering, the hyperbolic plane, then the averages of the lift g 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. We also consider averages over more general sets like arcs, tubes and horocycles.

math.CO↗