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Affine systems inL 2 (ℝd) II: Dual systems

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Abstract

The fiberization of affine systems via dual Gramian techniques, which was developed in previous papers of the authors, is applied here for the study of affine frames that have an affine dual system. Gramian techniques are also used to verify whether a dual pair of affine frames is also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of affine frames from an arbitrary MRA is obtained via the mixed extension principle.

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Authors and Affiliations

  1. Computer Science Department, University of Wisconsin-Madison, 1210 West Dayton Stret, 53706, Madison, Wisconsin

    Amos Ron

  2. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore

    Zuowei Shen

Authors
  1. Amos Ron
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  2. Zuowei Shen
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Additional information

This work was partially sponsored by the National Science Foundation under Grants DMS-9102857, DMS-9224748, and DMS-9626319, by the United States Army Research Office under Contracts DAAL03-G-90-0090, DAAH04-95-1-0089, and by the Strategic Wavelet Program Grant from the National University of Singapore.

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Ron, A., Shen, Z. Affine systems inL 2 (ℝd) II: Dual systems. The Journal of Fourier Analysis and Applications 3, 617–637 (1997). https://doi.org/10.1007/BF02648888

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  • DOI: https://doi.org/10.1007/BF02648888

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