Abstract
Fueter’s theorem (1934) asserts that every holomorphic intrinsic function of one complex variable induces an axial quaternionic monogenic function. Sce (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat 23:220–225, 1957) generalizes Fueter’s theorem to the Euclidean spaces \({{\mathbb {R}}}^{n+1}\) for n being odd positive integers. By using pointwise differential computation he asserted that every holomorphic intrinsic function of one complex variable induces an axial Clifford monogenic function for the cases n being odd. Qian (Rend Mat Acc Lincei 8:111–117, 1997) extended Sce’s result to both n being odd and even cases by using the corresponding Fourier multiplier operator when the required integrability is guaranteed, and the Kelvin inversion if not. For n being odd, Qian’s generalization coincides with Sce’s result based on the pointwise differential operator. In this paper, we unify these results in the distribution sense.
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Acknowledgements
Special thanks are due to Irene Sabadini who read the first draft of the note and gave valuable comments and suggestions. The study are partially funded by the Science and Technology Development Fund, Macau SAR (File no. 0123/2018/A3), and the National Natural Science Foundation of China (Grant No. 11901303).
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Dong, B., Qian, T. Uniform generalizations of Fueter’s theorem. Annali di Matematica 200, 229–251 (2021). https://doi.org/10.1007/s10231-020-00993-4
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DOI: https://doi.org/10.1007/s10231-020-00993-4