Convolution operators defined by singular measures on the motion group (Q2879950)

The authors start their consideration with some earlier results on the Radon type transform on \(\mathbb{R}^n\). The aim of the paper is to replace manifolds in \(\mathbb{R}^n\) with more general manifolds \(Y\) in \(\mathbb{R}^n\times\text{SO}(n)\). In order to deal with more general objects it is natural to work in the Euclidean motion group \(M_n\) rather than in \(\mathbb{R}^n\times\text{SO}(n)\) and to study the representation theory on \(M_n\).