On the Riesz bases, frames and minimal exponential systems in $L^2[-π,π]$.
Hokkaido Mathematical Journal, 40 (2011) pp.89-102
P. G. Casazza, O. Christensen, S. Li, and A. Lindner proved in  that some families of complex exponentials were either Riesz bases or not frames in $L^2[-π,π]$. First, we shall advance their results in this note. Sedletskii constructed in  an exponential system which is complete, minimal and not uniformly minimal with separable spectrum in $L^2[-π,π]$. Next, we shall construct a similar example with nonseparable spectrum in $L^2[-π,π]$.
|Uncontrolled Keywords||Riesz basis, frame, minimal, uniformly minimal|