Fourier uniqueness sets and the Klein-Gordon equation

Abstract: We generalize the study of Heisenberg uniqueness pairs considered in earlier work with Alfonso Montes-Rodriguez. We also find the critical density in the case of one branch of the hyperbola. In the critical case there is non-uniqueness for a one-dimensional space of solutions. These solutions cannot vanish at any other point of the axes of the characteristic lattice-cross, due to an unexpected connection with the Nielsen spiral.