Frames versus Riesz Bases

  • Ole Christensen
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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 fH, there exist coefficients {c k } k=1 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.


Hilbert Space Moment Problem Riesz Basis Tight Frame Frame Sequence 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Ole Christensen
    • 1
  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

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