1 citations · 3 across the 12 of their papers we have counts for
12 papers
Unitary rational functions: The scaled quaternion case
Daniel Alpay, Ilwoo Cho, Mihaela Vajiac
We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled…
Scaled global operators and Fueter variables on non-zero scaled hypercomplex numbers
Daniel Alpay, Ilwoo Cho, Mihaela Vajiac
In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbe…
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…
New Fueter Variables Associated to the Global Operator in the Quaternionic Case
Daniel Alpay, Kamal Diki, Mihaela Vajiac
The purpose of this paper is to develop a new theory of three non-commuting quaternionic variables and its related Schur analysis theory for a modified version of the quaternionic…
Two Bicomplex and One Multicomplex Least Mean Square algorithms
Daniel Alpay, Kamal Diki, Mihaela Vajiac
We study and introduce new gradient operators in the complex and bicomplex settings, inspired from the well-known Least Mean Square (LMS) algorithm invented in 1960 by Widrow and H…