Affine frames, GMRA's, and the canonical dual

• Autorzy: Marcin Bownik , Eric Weber
• Języki publikacji: EN

Abstrakty

EN

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 V₀ 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.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 46N99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 3
• Strony: 453-479

Daty

wydano

2003

Twórcy

autor

Marcin Bownik

• Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, U.S.A.
• Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A.

autor

Eric Weber

• Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036, U.S.A.
• Department of Mathematics, Iowa State University, Ames, IA 50011-2064, U.S.A.

Identyfikatory

DOI

10.4064/sm159-3-8