3 citations · 5 across the 17 of their papers we have counts for
7 papers · 1 filter
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…