Complementability of exponential systems (Q2338972)

The author proves the following to provide an affirmative answer to a question raised in [\textit{A. Nakamura}, Hokkaido Math. J. 36, No. 1, 193--206 (2007; Zbl 1138.42304)]. If \(\{e^{i\lambda t} :\lambda \in \Lambda \}\) is an incomplete system in \(L^2 (-\pi, \pi)\), then there exists a sequence \( T\subset \mathbb {R}\), \(\Lambda \cap T = \Phi \), such that the system \( S_{\Lambda \cup T}\) is complete and minimal in \(L^2 (- \pi, \pi)\).