Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg
  group   In this article, we prove that (unit sphere, non-harmonic cone) is a
Heisenberg uniqueness pair for the symplectic Fourier transform on $\mathbb
C^n.$ We derive that spheres as well as non-harmonic cones are determining sets
for the spectral projections of the finite measure supported on the unit
sphere. Further, we prove that if the Fourier transform of a finitely supported
function on step two nilpotent Lie group is of arbitrary finite rank, then the
function must be zero. The latter result correlates to the annihilating pair
for the Weyl transform.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ