Abstract
As we have seen, a frame {f k } ∞ k=1 in a Hilbert space H has one of the main properties of a basis: given f ∈ H, there exist coefficients {c k } ∞ k=1 ∈ ℓ 2(ℕ) such that f = ∑ ∞ k=1 c k f k . This makes it natural to study the relationship between frames and bases. We have already seen that Riesz bases are frames. In this chapter we exploit the relationship between these two concepts further. In particular, we give equivalent conditions for a frame to be a Riesz basis.
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© 2003 Springer Science+Business Media New York
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Christensen, O. (2003). Frames versus Riesz Bases. In: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8224-8_6
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DOI: https://doi.org/10.1007/978-0-8176-8224-8_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6500-9
Online ISBN: 978-0-8176-8224-8
eBook Packages: Springer Book Archive