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

Nakamura, Akihiro

Hokkaido Math. J. 36, No. 1, 193-206 (2007).

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

Keywords:

basis; Riesz basis; Riesz sequence; complete and minimal sequence