Range of the horocyclic Radon transform on trees
The authors describe the range of the horocyclic Radon transform \(R\) on a homogeneous tree \(T\). They first state the two Radon conditions, families of natural explicit relations for functions on the space \({\mathcal H}\) of horocycles of \(T\). They then show that, among compactly supported functions on \({\mathcal H}\), these conditions completely characterize the range of \(R\) on finitely supported functions on (the set of vertices of) \(T\). Similar descriptions are valid for the range of \(R\) on larger function spaces, although distributions on \({\mathcal H}\) need then to be taken into account. One of the theorems states that for \(s<1/\sqrt q\) the Radon transform is one-to-one on \(A_s\) and its range is \(B_s\).
scientific article; zbMATH DE number 1409069