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Characterization of Non-Stationary Wavelets and Non-Stationary Multiresolution Analysis Wavelets Related to Walsh Functions

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Abstract

The main aim of the present article is to provide a characteristic description of non-stationary orthonormal wavelets related to Walsh functions under some asymptotic conditions. We also provide the non-stationary multiresolution analysis and wavelets associated with non-stationary multiresolution analysis on the positive half-line. Further, we give a characterization of wavelets associated with such non-stationary multiresolution analysis on the positive half-line. Further, we give an example in support of our main result.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

The author is thankful to the reviewers for their valuable suggestions towards the improvement of the paper.

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Authors and Affiliations

  1. Zakir Husain Delhi College, University of Delhi, JLN Marg, New Delhi, 110 002, India

    Abdullah Abdullah

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  1. Abdullah Abdullah
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Correspondence to Abdullah Abdullah.

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Communicated by Sanne ter Horst, Dmitry S. Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.

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This article is part of the topical collection “Linear Operators and Linear Systems” edited by Sanne ter Horst, Dmitry S. Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.

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Abdullah, A. Characterization of Non-Stationary Wavelets and Non-Stationary Multiresolution Analysis Wavelets Related to Walsh Functions. Complex Anal. Oper. Theory 15, 86 (2021). https://doi.org/10.1007/s11785-021-01132-4

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