10 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…
Fractional -Laplacian of holomorphic functions via Jacobi polynomials
Fabrizio Colombo, Antonino De Martino, Alberto Debernardi Pinos
We give a distributional definition of the -fractional Laplacian for smooth functions with power-type singularities at the origin, including negative monomials and cer…
Representer Theorem in Complex Reproducing Kernel Hilbert Spaces with Applications to Fock and Hardy Spaces and Superoscillations
Natanael Alpay, Antonino De Martino, Kamal Diki
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (…
The resolvent equations for the Harmonic and bi-Harmonic functional calculi in dimension five
Fabrizio Colombo, Antonino De Martino, Joao Marques Da Costa
The fine structures on the -spectrum constitute a new research area that includes a class of functional calculi based on the -spectrum and on integral transforms determined b…
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…
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…