Diophantine integral geometry
The Radon transform of \(f\) is defined as the function \(R_{c}f:\mathbb{P}_{n}\to \mathbb{C}\) given by \[ R_{c}f(t,\omega)=\int_{H(t,\omega)}f(x)\,d\mu(x), \quad \text{for all}\quad (t,\omega)\in \mathbb{R}\times S^{n-1}, \] where \(d\mu\) is the Euclidean measure on the hyperplane \(H(t,\omega)\). The authors investigate the Radon transform \(R\) on discrete hyperplanes in the lattice \(\mathbb{Z}^{n}\) \((n\geq 2)\) defined by linear diophantine equations. More precisely, they study specific properties of the discrete Radon transform \(R\) and its dual \(R^{\ast}\), an inversion formula for \(R\) and an appropriate support theorem in the discrete case.
scientific article; zbMATH DE number 5292749