Cartwright-type theorems and real uniqueness sets for entire functions of exponential type (Q1326054)

Let \(E\subset \mathbb{R}^ n\) be a normalized set for given \(\sigma\), \(0<\sigma< \infty\), i.e. there is a finite constant \(C\) such that for any entire function \(f(z)\), \(z\subset \mathbb{C}^ n\), of exponential type at most \(\sigma\) the following inequality holds: \[ \sup\bigl\{| f(x)|: x\in \mathbb{R}^ n\bigr\}\leq C\sup\bigl\{| f(x)|: x\in E\bigr\}. \] The authors show that such normalized sets are uniqueness sets in a sense more stronger than usual.