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Spectral theorems associated with the (ka)-generalized wavelet multipliers

  • Hatem Mejjaoli
Article
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Abstract

We introduce the notion of the (ka)-generalized wavelet multipliers. Particular cases of such generalized wavelet multipliers are the classical and Dunkl wavelet multipliers. The restriction of the (ka)-generalized wavelet multipliers to radial functions is given by the generalized Hankel wavelet multiplier. We study the boundedness, Schatten class properties of the (ka)-generalized wavelet multipliers and we give them trace formula. We prove that the generalized Landau–Pollak–Slepian operator is a (ka)-generalized wavelet multiplier. Next, we give results on the boundedness and compactness of (ka)-generalized wavelet multipliers on \(L^{p}_{k,a}(\mathbb {R}^{d})\), \(1 \le p \le \infty \).

Keywords

\((k, a)\)-Laguerre semigroup \((k, a)\)-generalized Fourier transform \((k, a)\)-generalized multipliers \((k, a)\)-generalized two-wavelet multipliers Schatten-von Neumann class 

Mathematics Subject Classification

Primary 47G10 Secondary 42B10 47G30 

Notes

Acknowledgements

The author is deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article. The author thanks the professors K. Trimèche, M.W. Wong and S. Ben Said for their helps.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesTaibah UniversityAl Madinah Al MunawarahSaudi Arabia

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