3 citations · 5 across the 17 of their papers we have counts for
9 papers · 1 filter
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…
Functions and operators of the polyharmonic and polyanalytic Clifford fine structures on the -spectrum
Fabrizio Colombo, Antonino De Martino, Stefano Pinton
The spectral theory on the -spectrum originated to give quaternionic quantum mechanics a precise mathematical foundation and as a spectral theory for linear operators in vector…
Short-time Fourier transform and superoscillations
Daniel Alpay, Antonino De Martino, Kamal Diki +1
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and t…
New aspects of Bargmann transform using Touchard polynomials and hypergeometric functions
Daniel Alpay, Antonino De Martino, Kamal Diki
In this paper we study the ranges of the Schwartz space and its dual (space of tempered distributions) under the Segal-Bargmann transform. The char…
The harmonic -functional calculus based on the S-spectrum
Antonino de Martino, Stefano Pinton, Peter Schlosser
The aim of this paper is to introduce the -functional calculus for harmonic functions over the quaternions. More precisely, we give meaning to Df(T) for unbounded sectori…
Gaussian RBF-kernels via Fock spaces: quaternionic and several complex variables settings
Antonino De Martino, Kamal Diki
In this paper we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. Fi…
The Fueter-Sce mapping and the Clifford-Appell polynomials
Antonino De Martino, Kamal Diki, Ali Guzmán Adán
The Fueter-Sce theorem provides a procedure to obtain axially monogenic functions, which are in the kernel of generalized Cauchy-Riemann operator in . This resul…
A polyanalytic functional calculus of order 2 on the S-spectrum
Antonino De Martino, Stefano Pinton
The Fueter theorem provides a two step procedure to build an axially monogenic function, i.e. a null-solutions of the Cauchy-Riemann operator in , denoted by $ \math…
Compactness of localization operators on modulation spaces of -tempered distributions
Chiara Boiti, Antonino De Martino
We give sufficient conditions for compactness of localization operators on modulation spaces of -tempered distributions whose short-tim…