Heisenberg uniqueness pairs corresponding to finite number of parallel lines

TL;DR

This paper investigates conditions under which a finite set of parallel lines and a subset of real numbers form a Heisenberg uniqueness pair, providing necessary and sufficient conditions for such pairs.

Contribution

It introduces new necessary and sufficient conditions for Heisenberg uniqueness pairs involving finite parallel lines and subsets of real numbers.

Findings

Established necessary conditions for HUP with finite parallel lines.

Derived sufficient conditions for HUP in the same setting.

Enhanced understanding of the structure of HUP related to parallel lines.

Abstract

In this paper we study the Heisenberg uniqueness pairs corresponding to finite number of parallel lines $\Gamma$. We give a necessary condition and a sufficient condition for a subset $\Lambda$ of $\R$ so that $(\Gamma,\Lambda)$ becomes a HUP.