Gröchenig, Karlheinz

Localization of frames, Banach frames, and the invertibility of the frame operator

J. Fourier Anal. Appl. Vol.10 No.2 (2004) p.105-132, Zbl:1055.42018

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abstract

Several versions of localization of frames are introduced and studied in detail. One of the main features of localized frames is that they allow an automatic extension of the associated Hilbert space expansions to a class of Banach spaces. It is also proved that the dual frame inherits the localization properties of the frame. The results are applied to various sampling problems. The localization concepts described in the present paper are defined in terms of a choice of a Riesz basis for the underlying Hilbert space. In his later paper ``Localized frames are finite unions of Riesz sequences

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