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On the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames

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Abstract

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Deguang Han

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    David R. Larson

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  1. Deguang Han
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  2. David R. Larson
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Correspondence to Deguang Han.

Additional information

The second author was partially supported by NSF grant DMS-0139386.

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Han, D., Larson, D.R. On the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames. Acta Appl Math 107, 211–222 (2009). https://doi.org/10.1007/s10440-008-9420-2

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  • DOI: https://doi.org/10.1007/s10440-008-9420-2

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