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Time-Scale Localization Operators in the Weinstein Setting

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Abstract

Daubechies first used localization operators as a mathematical tool to localized a signal in the time frequency plane. They have been a subject of research in many domains ever since. In this paper, we introduce the notion of Weinstein two-wavelet and we define the two-wavelet localization operators in the setting of the Weinstein theory. Then, we give a host of sufficient conditions for the boundedness and compactness of the two-wavelet localization operator on \(L^{p}_{\alpha }(\mathbb {R}^{d+1}_+)\) for all \(1\le p\le \infty \), in terms of properties of the symbol \(\sigma \) and the functions \(\varphi \) and \(\psi \). In the end, we study some typical examples of the Weinstein two-wavelet localization operators.

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Acknowledgements

The author is deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article. The author extend him appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number “IF-2020-NBU-420”.

Funding

This research was funded by the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia through the project number “IF-2020-NBU-420”.

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  1. Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia

    Ahmed Saoudi

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Saoudi, A. Time-Scale Localization Operators in the Weinstein Setting. Results Math 78, 14 (2023). https://doi.org/10.1007/s00025-022-01792-4

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