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Dunkl–Weinstein Multiplier Operators and Applications to Reproducing Kernel Theory

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Abstract

In this paper, we have interested on the Dunkl–Weinstein multiplier operators \(\mathscr {M}_{k,\beta ,a}\) on the Dunkl–Weinstein-type Paley–Wiener space \(\mathscr {H}_s\). We give for these operators an application to the reproducing kernel theory; and we deduce for them best approximation on the Paley–Wiener space \(\mathscr {H}_s\). Finally, we give two applications in two particular cases, the first is a Weinstein case \((k=0)\), and the second is the Dunkl case when \(G=\mathbb {Z}_2^d\). More precisely, we write the solution of the Tikhonov regularization problem in these cases as a convolution product of two functions.

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Authors and Affiliations

  1. Faculté des Sciences de Tunis, Laboratoire d’Analyse Mathématique et Applications, Université de Tunis El Manar, LR11ES11, Tunis, 2092, Tunisia

    Fethi Soltani & Ibrahim Maktouf

  2. Ecole Nationale d’Ingénieurs de Carthage, Université de Carthage, Tunis, 2035, Tunisia

    Fethi Soltani

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  1. Fethi Soltani
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  2. Ibrahim Maktouf
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Professor Fethi Soltani is the superviser of Ibrahim Maktouf. Then, this work is solved by Ibrahim Maktouf and it is editing by Professor Fethi Soltani.

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Correspondence to Fethi Soltani.

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Soltani, F., Maktouf, I. Dunkl–Weinstein Multiplier Operators and Applications to Reproducing Kernel Theory. Mediterr. J. Math. 21, 80 (2024). https://doi.org/10.1007/s00009-024-02623-2

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  • DOI: https://doi.org/10.1007/s00009-024-02623-2

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