# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 36 (2007) pp.193-206

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### Abstract

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 $L^2[-\pi,\pi]$.

MSC(Primary) 42C15 42C99, 42C30 Riesz basis, Riesz sequence, complete and minimal sequence