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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.FA2025
Polyanalytic Gaussian Radial Basis Function Kernel and Itô-Hermite Polynomials
Hendrik De Bie, Antonino De Martino, Kamal Diki
We introduce a polyanalytic extension of the Gaussian radial basis function (RBF) kernel by computing the action of the convolution operator on normalized Hermite functions. In par…
math.FA2025
On the harmonic generalized Cauchy-Kovalevskaya extension and its connection with the Fueter-Sce theorem
Antonino De Martino, Ali Guzmán Adán
One of the primary objectives of this paper is to establish a generalized Cauchy-Kovalevskaya extension for axially harmonic functions. We demonstrate that the result can be expres…