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Time–frequency Analysis Associated with Some Partial Differential Operators

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Abstract

In this paper, we prove the boundedness and compactness of localization operators associated with Riemann–Liouville wavelet transforms, which depend on a symbol and two Riemann–Liouville wavelets on \(L^{p}(\mathrm{d}\nu _{_{\alpha }})\), \(1 \le p \le \infty \). Next, we establish Shapiro’s mean dispersion-type theorems and we study the scalogram for the same wavelet 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.

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Authors and Affiliations

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

    Hatem Mejjaoli

  2. Departement of mathematics, Institut préparatoire aux études d’ingénieur, Campus universitaire El Manar, Tunis, 2092, Tunisie

    Slim Omri

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  1. Hatem Mejjaoli
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  2. Slim Omri
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Correspondence to Slim Omri.

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Mejjaoli, H., Omri, S. Time–frequency Analysis Associated with Some Partial Differential Operators. Mediterr. J. Math. 15, 161 (2018). https://doi.org/10.1007/s00009-018-1198-5

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  • DOI: https://doi.org/10.1007/s00009-018-1198-5

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