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Characterization of wavelets and MRA wavelets on local fields of positive characteristic

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Abstract

We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi-affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic equations. We also give another characterization of wavelets. Further, all wavelets which are associated with a multiresolution analysis on such a local field are also characterized.

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Acknowledgments

We thank the referee for his/her thorough review and highly appreciate the comments and suggestions, which significantly contributed to improving the overall presentation of the article.

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Authors and Affiliations

  1. Statistics and Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India

    Biswaranjan Behera & Qaiser Jahan

Authors
  1. Biswaranjan Behera
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  2. Qaiser Jahan
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Correspondence to Biswaranjan Behera.

Additional information

Research of Q. Jahan is supported by a grant from CSIR, India.

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Behera, B., Jahan, Q. Characterization of wavelets and MRA wavelets on local fields of positive characteristic. Collect. Math. 66, 33–53 (2015). https://doi.org/10.1007/s13348-014-0116-9

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  • DOI: https://doi.org/10.1007/s13348-014-0116-9

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