Abstract
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 a number of equivalent conditions for a frame to be a Riesz basis.
We have often spoken about a frame in an intuitive sense as some kind of “overcomplete basis.” It turns out that, in the technical sense, one has to be careful with such statements. In fact, we will prove the existence of a frame which has no relation to a basis: no subfamily of the frame forms a basis. On the other hand, sufficient conditions for a frame to contain a Riesz basis as a subfamily are also given.
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Christensen, O. (2016). Frames Versus Riesz Bases. In: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-25613-9_7
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DOI: https://doi.org/10.1007/978-3-319-25613-9_7
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