Mathematische Annalen

, Volume 332, Issue 4, pp 705–720 | Cite as

On the existence of multiresolution analysis for framelets

Article

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.

Mathematics Subject Classification (2000)

42C40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OregonEugeneUSA
  2. 2.Mathematical InstituteUniversity of WrocławWrocławPoland
  3. 3.Department of MathematicsUniversity of OregonEugeneUSA

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