10 citations · 48 across the 53 of their papers we have counts for
6 papers · 2 filters
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…
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…
Commuting operators over Pontryagin spaces with applications to system theory
Daniel Alpay, Ariel Pinhas, Victor Vinnikov
In this paper we extend vessel theory, or equivalently, the theory of overdetermined systems to the Pontryagin space setting. We focus on realization theorems of the various c…
Generalized Fock spaces and the Stirling numbers
Daniel Alpay, Motke Porat
The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Ge…
Realizations of holomorphic and slice hyperholomorphic functions: the Krein space case
Daniel Alpay, Fabrizio Colombo, Irene Sabadini
In this work we treat realization results for operator-valued functions which are analytic in the complex sense or slice hyperholomorphic over the quaternions. In the complex setti…