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• W4200633735 abstract "The Fueter-Sce-Qian (FSQ for short) mapping theorem is a two-steps procedure to extend holomorphic functions of one complex variable to slice monogenic functions and to monogenic functions. Using the Cauchy formula of slice monogenic functions the FSQ-theorem admits an integral representation for n odd. In this paper we show that the relation Δn+1(n−1)/2SL−1=FnL between the slice monogenic Cauchy kernel SL−1 and the F-kernel FnL, that appear in the integral form of the FSQ-theorem for n odd, holds also in the case we consider the fractional powers of the Laplace operator Δn+1 in dimension n+1, i.e., for n even. Moreover, this relation is proven computing explicitly the Fourier transform of the kernels SL−1 and FnL as functions of the Poisson kernel. Similar results hold for the right kernels SR−1 and of FnR." @default.
• W4200633735 created "2021-12-31" @default.
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• W4200633735 date "2022-08-01" @default.
• W4200633735 modified "2023-09-30" @default.
• W4200633735 title "The Poisson kernel and the Fourier transform of the slice monogenic Cauchy kernels" @default.
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• W4200633735 doi "https://doi.org/10.1016/j.jmaa.2022.126115" @default.
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