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 [Inverse and ill-posed problems series, VSP, Utrecht, 1994] to describe the kernel of the integral moment transforms over symmetric m m -tensor fields in n n -dimensional Euclidean space. We also provide an equivalence between the injectivity question for the integral moment transforms and generalized Saint Venant operator over symmetric tensor fields of Schwartz class.