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Wave packet transform and wavelet convolution product involving the index Whittaker transform

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Abstract

The main goal of this paper is to study the wave packet transform (WPT) and wavelet convolution product involving the index Whittaker transform (IWT). Some estimates for the Whittaker wavelet (W-Wavelet) and W-wavelet transform are obtained, and Plancherel’s relation for the WPT-transform is also deduced. Calderón’s formula associated with IWT is obtained. Furthermore, using the convolution property of IWT, the wavelet convolution product is defined, and some related results are discussed.

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Acknowledgements

The authors are very grateful to anonymous reviewer for his/her constructive and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India

    Jeetendrasingh Maan & Akhilesh Prasad

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  1. Jeetendrasingh Maan
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  2. Akhilesh Prasad
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Contributions

JM: Solving the problems, Writing the manuscript. AP: Suggested the problems, Suggested Methodology.

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Correspondence to Akhilesh Prasad.

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Maan, J., Prasad, A. Wave packet transform and wavelet convolution product involving the index Whittaker transform. Ramanujan J 64, 19–36 (2024). https://doi.org/10.1007/s11139-023-00793-3

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