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Quantitative Uncertainty Principles Associated with the k-Generalized Stockwell Transform

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Abstract

In this paper, we introduce the k-generalized Stockwell transform on \({\mathbb {R}}\). We investigate for this transform the main theorems of Harmonic analysis as Plancherel’s, Calderón’s, and inversion formulas. Next, we prove several uncertainty principles for this transform such as Heisenberg’s type inequalities, Shannon’s uncertainty principle, Benedick–Amrein–Berthier’s uncertainty principle, and local uncertainty principles. Finally, after reviewing the k-generalized weighted inequalities, we connect these inequalities to show a generalization of uncertainty principles for the k-generalized Stockwell transform.

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Acknowledgements

The authors are deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article. The first author would like to thank professor MW. Wong for his help.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Taibah University, PO BOX 30002, Al Madinah Al Munawarah, Saudi Arabia

    Hatem Mejjaoli

  2. Department of Mathematics, Faculty of Sciences of Tunis, Tunis El Manar University, CAMPUS, 2092, Tunis, Tunisia

    Khalifa Trimèche

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  1. Hatem Mejjaoli
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  2. Khalifa Trimèche
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Correspondence to Khalifa Trimèche.

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Mejjaoli, H., Trimèche, K. Quantitative Uncertainty Principles Associated with the k-Generalized Stockwell Transform. Mediterr. J. Math. 19, 150 (2022). https://doi.org/10.1007/s00009-021-01968-2

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