In this note, we show that some families of complex exponentials are either Riesz sequences or not basic sequences in $L^2[-\pi,\pi]$. Besides, we show that every incomplete complex exponential system satisfying some condition can be complemented up to a complete and minimal system of complex exponentials in $L^2[-\pi,\pi]$.
"Basis properties and complements of complex exponential systems." Hokkaido Math. J. 36 (1) 193 - 206, February 2007. https://doi.org/10.14492/hokmj/1285766658