10 citations · 37 across the 40 of their papers we have counts for
12 papers · 1 filter
A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics
Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and…
The Fock space as a de Branges-Rovnyak space
Daniel Alpay, Fabrizio Colombo, Irene Sabadini
We show that de Branges-Rovnyak spaces include as special cases a number of spaces, such as the Hardy space, the Fock space, the Hardy-Sobolev space and the Dirichlet space. We pre…
On slice polyanalytic functions of a quaternionic variable
Daniel Alpay, Kamal Diki, Irene Sabadini
In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quate…
Realization of tensor-product and of tensor-Factorization of rational functions
Daniel Alpay, Izchak Lewkowicz
We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressi…
Positive and generalized positive real lemma for slice hyperholomorphic functions
D. Alpay, F. Colombo, I. Lewkowicz +1
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic function…
Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra
Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the -norm. We focus on the rational case. We start with…