Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group

Somnath Ghosh, R. K. Srivastava

Published 2018-10-11Version 1

In this article, we prove that a non-harmonic cone is Heisenberg uniqueness pair corresponding to the unit sphere for the symplectic Fourier transform on $\mathbb C^n.$ Further, we derive that a sphere whose radius is not contained in the zero set of the Laguerre polynomials is a determining set for the spectral projections of the finite measure supported on the unit sphere. Finally, we give a simple proof a Benedick-Amrein-Berthier type theorem for the Heisenberg group using twisted translations.