On the Riesz bases, frames and minimal exponential systems in L2[-π,π]

Abstract

P. G. Casazza, O. Christensen, S. Li, and A. Lindner proved in [3] that some families of complex exponentials were either Riesz bases or not frames in L²[-π,π]. First, we shall advance their results in this note. Sedletskii constructed in [9] an exponential system which is complete, minimal and not uniformly minimal with separable spectrum in L²[-π,π]. Next, we shall construct a similar example with nonseparable spectrum in L²[-π,π].