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Deficits and Excesses of Frames

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Abstract

The excess of a sequence in a Hilbert space is the greatest number of elements that can be removed yet leave a set with the same closed span. We study the excess and the dual concept of the deficit of Bessel sequences and frames. In particular, we characterize those frames for which there exist infinitely many elements that can be removed from the frame yet still leave a frame, and we show that all overcomplete Weyl–Heisenberg and wavelet frames have this property.

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Authors and Affiliations

  1. Siemens Corporate Research, Princeton, NJ, 08540, USA

    Radu Balan

  2. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Peter G. Casazza

  3. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Christopher Heil

  4. Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA, 94720, USA

    Zeph Landau

Authors
  1. Radu Balan
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  2. Peter G. Casazza
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  3. Christopher Heil
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  4. Zeph Landau
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Correspondence to Christopher Heil.

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Balan, R., Casazza, P.G., Heil, C. et al. Deficits and Excesses of Frames. Advances in Computational Mathematics 18, 93–116 (2003). https://doi.org/10.1023/A:1021360227672

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  • DOI: https://doi.org/10.1023/A:1021360227672

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