A+ CATEGORY SCIENTIFIC UNIT

Affine frames, GMRA's, and the canonical dual

Volume 159 / 2003

Marcin Bownik, Eric Weber Studia Mathematica 159 (2003), 453-479 MSC: Primary 42C40, 46N99. DOI: 10.4064/sm159-3-8

Abstract

We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace $V_0$ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine frame has the quasi-affine structure.

Authors

  • Marcin BownikDepartment of Mathematics
    University of Michigan
    Ann Arbor, MI 48109-1109, U.S.A.
    and
    Department of Mathematics
    University of Oregon
    Eugene, OR 97403-1222, U.S.A.
    e-mail
    e-mail
  • Eric WeberDepartment of Mathematics
    University of Wyoming
    Laramie, WY 82071-3036, U.S.A.
    and
    Department of Mathematics
    Iowa State University
    Ames, IA 50011-2064, U.S.A.
    e-mail

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