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Semi-orthogonal Parseval Wavelets Associated with GMRAs on Local Fields of Positive Characteristic

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Abstract

In this article, we establish theory of semi-orthogonal Parseval wavelets associated with generalized multiresolution analysis (GMRA) for local fields of positive characteristics (LFPC) and obtain their characterization in terms of consistency equation. As a consequence, we obtain a characterization of an orthonormal (multi)wavelet associated with an MRA in terms of multiplicity function as well as dimension function. Further, we provide characterizations of Parseval scaling functions, scaling sets and bandlimited wavelets together with a Shannon-type multiwavelet. Some examples of such wavelets are also produced for LFPC.

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Acknowledgements

The authors would like to thank all the anonymous reviewers for providing fruitful suggestions to improve the presentation of this article. The first and second authors were supported by NBHM (DAE) grant-14723 and TEQIP-III, NPIU (MHRD), respectively, during the revision of manuscript.

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  1. Saurabh Chandra Maury

    Present address: Department of Applied Mathematics and Computational Science, SGSITS, Indore, India

Authors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, India

    Niraj K. Shukla

  2. Department of Mathematics and Statistical Sciences, S. R. M. University, Lucknow, India

    Saurabh Chandra Maury

  3. Department of Mathematics, S.P.M. Govt. Degree College, Prayagraj, India

    Shiva Mittal

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  1. Niraj K. Shukla
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  2. Saurabh Chandra Maury
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Correspondence to Niraj K. Shukla.

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Shukla, N.K., Maury, S.C. & Mittal, S. Semi-orthogonal Parseval Wavelets Associated with GMRAs on Local Fields of Positive Characteristic. Mediterr. J. Math. 16, 120 (2019). https://doi.org/10.1007/s00009-019-1383-1

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  • DOI: https://doi.org/10.1007/s00009-019-1383-1

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