The Radon transform on abelian groups
Let A be a finite group and let B be a subset of A. For any function \(f: A\to {\mathbb{C}}\), one can define the function \(F_ B: A\to {\mathbb{C}}\), called the Radon transform of f with respect to B by \(F_ B(a):=\sum_{b\in B}f(ab)\). The problem we address in this note is: for which subsets B is the Radon transform invertible ? Our main result gives a combinatorial description of such B in the case \(A={\mathbb{Z}}^ n_ 2\).
scientific article; zbMATH DE number 3981782