Uniqueness of the Fourier transform on the Euclidean motion group

Abstract

In this article, we prove that if the Fourier transform of a certain integrable function on the Euclidean motion group is of finite rank, then the function has to vanish identically. Further, we explore a new variance of the uncertainty principle, the Heisenberg uniqueness pairs on the Euclidean motion group as well as on the product group ${\mathbb{R}}^n\times K,$ where $K$ is a compact group.

19 pages, minor update

References in corpus (1)

• Heisenberg uniqueness pairs for some algebraic curves and surfaces