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Basis properties and complements of complex exponential systems. (English) Zbl 1138.42304

Summary: 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:

42C15 General harmonic expansions, frames
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
42C99 Nontrigonometric harmonic analysis
42A65 Completeness of sets of functions in one variable harmonic analysis
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