, Volume 332, Issue 4, pp 705-720
Date: 07 May 2005

On the existence of multiresolution analysis for framelets

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Abstract

We show that a compactly supported tight framelet comes from an MRA if the intersection of all dyadic dilations of the space of negative dilates, which is defined as the shift-invariant space generated by the negative scales of a framelet, is trivial. We also construct examples of (non-tight) framelets, which are arbitrarily close to tight frame framelets, such that the corresponding space of negative dilates is equal to the entire space L 2ℝ.

The first author was partially supported by the NSF grant DMS–0441817