On the existence of multiresolution analysis for framelets
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- Bownik, M. & Rzeszotnik, Z. Math. Ann. (2005) 332: 705. doi:10.1007/s00208-005-0645-3
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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.