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Pseudo Wavelet Frames

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Abstract

We seek to alleviate the unpleasantness of the fact that the class of wavelet frames is not closed under canonical duals by introducing and studying a new class of frames that we call pseudo wavelet frames, which includes all wavelet frames and is ‘self-dual’ in terms of canonical duals. The class also has the ‘extension property’ and is invariant under the Fourier transform.

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Acknowledgements

The authors are thankful to the anonymous referee for pertinent comments that improved the overall presentation of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Government Brennen College, Dharmadam, Thalassery, Kerala, 670106, India

    T. C. Easwaran Nambudiri

  2. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, 600005, India

    K. Parthasarathy

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  1. T. C. Easwaran Nambudiri
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  2. K. Parthasarathy
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Correspondence to T. C. Easwaran Nambudiri.

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Nambudiri, T.C.E., Parthasarathy, K. Pseudo Wavelet Frames. Acta Math Vietnam 45, 931–941 (2020). https://doi.org/10.1007/s40306-020-00387-x

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  • DOI: https://doi.org/10.1007/s40306-020-00387-x

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