The generalized Saint Venant operator and integral moment transforms

Abstract: In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov to describe the kernel of the integral moment transforms over symmetric m-tensor fields in n-dimensional Euclidean space. We also provide an equivalence between the injectivity question for the integral moment transforms and the generalized Saint Venant operator over symmetric tensor fields of the Schwartz class.