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math.FA2026
A variation of the inverse Fueter theorem and the generalized polyanalytic Cauchy-Kovalevskaya extension of order 2
Antonino De Martino, Stefano Pinton
In this paper, we first establish a generalized Cauchy--Kovalevskaya (GCK) extension for axially polyanalytic functions of order . We prove that the extension can be written as…
math.FA2026
A unified approach to the Dirac fine structures on the -spectrum and a connection with Gegenbauer polynomials
F. Colombo, A. De Martino, S. Pinton
This paper contributes to the recently introduced theory of fine structures on the -spectrum. We study, in a unified way, the functional calculi for axially Poly-Analytic-Harmon…
math.FA2026
On the application of the factorized Fueter-Sce map to the slice hyperholomorphic Cauchy kernel
Antonino De Martino, Stefano Pinton
The Fueter-Sce theorem is one of the most important results in hypercomplex analysis, providing a two-step procedure for constructing axially monogenic functions starting from holo…