On the excess of a sequence of exponentials with perturbations at some subsequences of integers (Q1587239)

A system of complex exponentials \(\{e^{i\lambda_n t}\}_{n\in \mathbb Z}\) is said to be minimal in \(L^2[-\pi ,\pi ]\) if each element of the system lies outside the closed linear span of the others. The system \(\{e^{i\lambda_n t}\}_{n\in \mathbb Z}\) has excess \(N\) if it remains complete and becomes minimal when \(N\) terms are removed and it has excess \(-N\) if it becomes complete and minimal when \(N\) terms are adjoined. In this article the excess is calculated of a sequence of exponentials with perturbations at some subsequences of integers.