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

  • Niraj K. ShuklaEmail author
  • Saurabh Chandra Maury
  • Shiva Mittal
Article
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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.

Keywords

Local fields translation invariant spaces multiplicity function semi-orthogonal Parseval wavelets bandlimited wavelets 

Mathematics Subject Classification

42C40 42C15 43A70 11S85 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Niraj K. Shukla
    • 1
    Email author
  • Saurabh Chandra Maury
    • 2
    • 3
  • Shiva Mittal
    • 4
  1. 1.Discipline of MathematicsIndian Institute of Technology IndoreIndoreIndia
  2. 2.Department of Mathematics and Statistical SciencesS. R. M. UniversityLucknowIndia
  3. 3.Department of Applied Mathematics and Computational ScienceSGSITSIndoreIndia
  4. 4.Department of MathematicsS.P.M. Govt. Degree CollegePrayagrajIndia

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