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The Fourier Transform Associated to the k-Hyperbolic Dirac Operator

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Abstract

The polynomial null solutions of the k-hyperbolic Dirac operator are investigated by the \(\mathfrak {osp}(1|2)\) approach. These solutions are then utilized to construct the (fractional) Fourier transform associated to the k-hyperbolic Dirac operator. The resulting integral kernels are found to be a specific kind of Dunkl kernels. Additionally, we give tight uncertainty inequalities for three distinct fractional Fourier transforms that we have defined. These inequalities are new even for the ordinary fractional Hankel and Weinstein transforms.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

Funding

This work was supported by the Tianjin Municipal Commission of Education (no. 2021KJ180) and Tianjin Municipal Science and Technology Commission (no. 22JCQNJC00470).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tianjin Normal University, Binshui West Road 393, Tianjin, 300387, People’s Republic of China

    Wenxin Li & Pan Lian

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  1. Wenxin Li
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  2. Pan Lian
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Correspondence to Pan Lian.

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Communicated by Uwe Kaehler.

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Li, W., Lian, P. The Fourier Transform Associated to the k-Hyperbolic Dirac Operator. Adv. Appl. Clifford Algebras 33, 26 (2023). https://doi.org/10.1007/s00006-023-01274-y

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