8 papers
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…
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…
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…
An introduction to the fine structures on the -spectrum
Fabrizio Colombo, Antonino De Martino, Stefano Pinton +2
Holomorphic functions are fundamental in operator theory and their Cauchy formula is a crucial tool for defining functions of operators. The Fueter-Sce extension theorem (often cal…
On the connection between the Fueter-Sce-Qian theorem and the generalized CK-extension
Antonino De Martino, Kamal Diki, Alí Guzmán Adán
The Fueter-Sce-Qian theorem provides a way of inducing axial monogenic functions in from holomorphic intrinsic functions of one complex variable. This result was…
The Poisson kernel and the Fourier transform of the slice monogenic Cauchy kernels
Fabrizio Colombo, Antonino De Martino, Tao Qian +1
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 f…
On the polyanalytic short-time Fourier transform in the quaternionic setting
Antonino De Martino, Kamal Diki
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the rece…
On the Quadratic Cone of
Cinzia Bisi, Antonino De Martino
In this paper we study the following type of functions , where is the quadratic cone of the algebr…