Geodesic
Affine frames, GMRA's, and the canonical dual
Marcin Bownik 1   ; Eric Weber 2
1 Department 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.
2 Department 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.
Studia Mathematica, Tome 159 (2003) no. 3, pp. 453-479 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm159-3-8
Keywords: canonical dual affine frame has affine structure number generators core subspace shift invariant demonstrate however converse apply results setting oversampling affine frames computing period riesz wavelet answering affirmative conjecture daubechies han additionally completely characterize canonical dual quasi affine frame has quasi affine structure

Marcin Bownik  1   ; Eric Weber  2

1 Department 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.
2 Department 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. 
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Marcin Bownik; Eric Weber. Affine frames, GMRA's, and the canonical dual. Studia Mathematica, Tome 159 (2003) no. 3, pp. 453-479. doi: 10.4064/sm159-3-8

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