Hokkaido Mathematical Journal

Nakamura Akihiro,

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 [3] 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 [9] 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 $L^2[-π,π]$.

MSC(Secondary)42C99, 42C30
Uncontrolled KeywordsRiesz basis, frame, minimal, uniformly minimal