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Some results on g-frames in Hilbert spaces. (English) Zbl 1242.41030
Summary: We show that every g-frame for a Hilbert space can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for . We further give necessary and sufficient conditions on g-Bessel sequences {Λ i (, i ):iJ} and {Γ i (, i ):iJ} and operators L 1 , L 2 on so that {Λ i L 1 +Γ i L 2 :iJ} is a g-frame for . We next show that a g-frame can be added to any of its canonical dual g-frame to yield a new g-frame.
MSC:
41A58Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
42C15General harmonic expansions, frames