3 citations · 5 across the 17 of their papers we have counts for
18 papers
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…
New Taylor and Laurent series of axially harmonic, Fueter regular and polyanalytic functions
Fabrizio Colombo, Antonino De Martino, Irene Sabadini
The Fueter-Sce mapping theorem stands as one of the most profound outcomes in complex and hypercomplex analysis, producing hypercomplex generalizations of holomorphic functions. In…
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 Bicomplex Tensor Product, a Bicomplex Choi Theorem and Applications
Daniel Alpay, Antonino De Martino, Kamal Diki +1
In this paper we extend the concept of tensor product to the bicomplex case and use it to prove the bicomplex counterpart of the classical Choi theorem in the theory of complex mat…
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…
Harmonic and polyanalytic functional calculi on the -spectrum for unbounded operators
Fabrizio Colombo, Antonino De Martino, Stefano Pinton
Harmonic and polyanalytic functional calculi have been recently defined for bounded commuting operators. Their definitions are based on the Cauchy formula of slice hyperholomorphic…
The fine structure of the spectral theory on the -spectrum in dimension five
Fabrizio Colombo, Antonino De Martino, Stefano Pinton +1
Holomorphic functions play a crucial role in operator theory and the Cauchy formula is a very important tool to define functions of operators. The Fueter-Sce-Qian extension theorem…
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…
Generalized Appell polynomials and Fueter-Bargmann transforms in the polyanalytic setting
Antonino De Martino, Kamal Diki
Tnis paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings it…
The -resolvent equation and Riesz projectors for the -functional calculus
Fabrizio Colombo, Antonino De Martino, Irene Sabadini
The Fueter-Sce-Qian mapping theorem is a two steps procedure to extend holomorphic functions of one complex variable to quaternionic or Clifford algebra-valued functions in the ker…
On the Clifford short-time Fourier transform and its properties
Antonino De Martino
In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of the main properties of the Clifford short-time Fourier tra…
On a Runge Theorem over
Cinzia Bisi, Antonino de Martino, Joerg Winkelmann
In this paper we investigate a topological characterization of the Runge theorem in the Clifford algebra via the description of the homology groups of axially symme…
On Brolin's theorem over the quaternions
Cinzia Bisi, Antonino De Martino
In this paper we investigate the Brolin's theorem over , the skew field of quaternions. Moreover, considering a quaternionic polynomial with real coefficients, we f…
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…