On the Connection Between the Fueter–Sce–Qian Theorem and the Generalized CK-Extension

The Fueter–Sce–Qian theorem provides a way of inducing axial monogenic functions in $$\mathbb {R}^{m+1}$$ from holomorphic intrinsic one complex variable. This result was initially proved by Fueter and Sce for the cases where dimension m is odd using pointwise differentiation, while extension to even Qian corresponding Fourier multipliers. In this paper, we provide an alternative description terms generalized CK-extension. latter characterizes null solutions Cauchy–Riemann operator their restrictions real line. leads one-to-one correspondence between space axially analytic We explicit expressions map CK-extension both cases, odd. These allow plane wave decomposition or, more particular, factorization mapping dual Radon transform. turn, new possibility extending Coherent State Transform (CST) Clifford Analysis. construct CST defined through mapping, show how it related slice CST’s already studied literature.