The generalized Saint Venant operator and integral moment transforms

TL;DR

This paper explores the generalized Saint Venant operator to understand the kernel of integral moment transforms on symmetric tensor fields, establishing an equivalence with the injectivity problem in Euclidean space.

Contribution

It introduces a generalized Saint Venant operator for symmetric tensor fields and links it to the injectivity of integral moment transforms, advancing the theoretical understanding.

Findings

Characterization of the kernel of integral moment transforms

Equivalence between injectivity and the generalized Saint Venant operator

Framework applicable to symmetric m-tensor fields in Euclidean space

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.