Mathematische Annalen

, Volume 332, Issue 4, pp 705–720

On the existence of multiresolution analysis for framelets


DOI: 10.1007/s00208-005-0645-3

Cite this article as:
Bownik, M. & Rzeszotnik, Z. Math. Ann. (2005) 332: 705. doi:10.1007/s00208-005-0645-3


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)


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