On the existence of multiresolution analysis for framelets |
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| Authors: | Marcin?Bownik mailto:mbownik@uoregon.edu" title=" mbownik@uoregon.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Ziemowit?Rzeszotnik |
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| Affiliation: | (1) Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA;(2) Mathematical Institute, University of Wrocław, 2/4, Pl. Grunwaldzki, 50-384 Wrocław, Poland;(3) Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA |
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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 |
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| Keywords: | 42C40 |
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