Heisenberg uniqueness pairs for the measure supported on the finite parallel lines
Deb Kumar Giri, Hiranmoy Pal, R. K. Srivastava · arXiv (Cornell University) · 2016
A Heisenberg uniqueness pair is a pair $\left(\Gamma, \Lambda\right)$, where $\Gamma$ is a smooth curve or a finite disjoint union of smooth curves and $\Lambda\subset\mathbb R^2$ is such that any finite Borel measure $\mu$ with support on $\Gamma$ and absolutely continuous with respect to the arc length of $\Gamma$ for which Fourier transform $\hat\mu\vert_\Lambda=0,$ implies $\mu=0.$ In this article, we find a characterization of the Heisenberg uniqueness pairs corresponding to finite number of parallel lines. In the latter case, we observe a phenomenon of interlacing of finite number of dispensable sets.