Benedick's theorem for the Heisenberg group

Abstract

If $f$ is a compactly supported function on the Heisenberg group and the group Fourier transform $\hat{f}(\lambda )$ is a finite rank operator for all $\lambda$ then $f$ is the zero function.

Cited by in corpus (5)

• Non-harmonic cones are Heisenberg uniqueness pairs for the Fourier transform on ${\mathbb{R}}^n$
• Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group
• Benedicks-Amrein-Berthier theorem for the Heisenberg motion group and quaternion Heisenberg group
• Heisenberg uniqueness pairs for some algebraic curves and surfaces
• Heisenberg uniqueness pairs for some algebraic curves in the plane