Uniqueness of the group Fourier transform on certain nilpotent Lie groups

2016/07/13 by Chattopadhyay, A., Giri, D. K., Srivastava, R. K.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1607.03832

Abstract

In this article, we prove that if the group Fourier transform of certain integrable functions on the Heisenberg motion group (or step two nilpotent Lie groups) is of finite rank, then the function is identically zero. These results can be thought as an analogue to the Benedicks theorem that dealt with the uniqueness of the Fourier transform of integrable functions on the Euclidean spaces.

Related

• Uniqueness of the Fourier transform on the Euclidean motion group
• Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group
• Benedick's theorem for the Heisenberg group
• Benedicks-Amrein-Berthier theorem for the Heisenberg motion group and quaternion Heisenberg group
• A Frequency Space for the Heisenberg Group