The horocyclic Radon transform on non-homogeneous trees (Q1802748)

The paper considers the horocyclic Radon transform on a general (infinite) tree \(T\). A horocycle is a set of vertices defined by means of distances from a fixed path in the tree \(T\). The horocycles define a partition of the vertex set \(V(T)\). The horocyclic Radon transform on \(T\) is defined for all functions \(f\in L^ 1(T)\) as \[ Rf(h)=\sum_{v\in h}f(v)\quad\text{for every horocycle } h\in{\mathcal H}. \] The Radon transform is proved to be injective on \(L^ 1(T)\), and its inverse transform is given. A function can be reconstructed too from the values on the horocycles.