23 citations · 40 across the 30 of their papers we have counts for
6 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…
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-Real Calculus and Applications to Bicomplex Hermite-Itô Polynomials
Daniel Alpay, Kamal Diki, Mihaela Vajiac
In this paper we extend notions of complex C-R-calculus and complex Hermite polynomials to the bicomplex setting and compare the bicomplex polyanalytic function theory to the class…
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…
Superoscillations and Fock spaces
Daniel Alpay, Fabrizio Colombo, Kamal Diki +2
In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences…