24 citations · 100 across the 17 of their papers we have counts for
23 papers
A note on irreducible slice algebraic sets
Anna Gori, Giulia Sarfatti, Fabio Vlacci
In this short note we prove that if is a right radical and quasi prime ideal in the ring of quaternionic slice regular polynomials, then the symmetrization …
On the irreducibility of slice algebraic sets
Anna Gori, Giulia Sarfatti, Fabio Vlacci
In the present paper we investigate the relations between irreducible slice algebraic sets in and quasi prime right ideals of the ring of slice regular polynomials i…
Resultants of slice regular polynomials in two quaternionic variables
Anna Gori, Giulia Sarfatti, Fabio Vlacci
We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant.We use this tool to inve…
A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables
Anna Gori, Giulia Sarfatti, Fabio Vlacci
In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring of slice regular polynomials in several quaternionic variables. Our p…
Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials
Anna Gori, Giulia Sarfatti, Fabio Vlacci
We study the vanishing sets of slice regular polynomials in several quaternionic variables. We obtain a geometric description of the vanishing sets in two variables, which leads to…
On compact affine quaternionic curves and surfaces
Graziano Gentili, Anna Gori, Giulia Sarfatti
This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that…
Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt +1
We characterize the Carleson measures for the Dirichlet space on the bidisc, hence also its multiplier space. Following Maz'ya and Stegenga, the characterization is given in terms…
Quaternionic inner and outer functions
Alessandro Monguzzi, Giulia Sarfatti, Daniel Seco
We study properties of inner and outer functions in the Hardy space of the quaternionic unit ball. In particular, we give sufficient conditions as well as necessary ones for functi…
Shift invariant subspaces of slice functions
Alessandro Monguzzi, Giulia Sarfatti
In this paper we characterize the closed invariant subspaces for the (-)multiplier operator of the quaternionic space of slice functions. As a consequence, we obtain the i…
Slice-Polynomial Functions and Twistor Geometry of Ruled Surfaces in
Amedeo Altavilla, Giulia Sarfatti
In the present paper we introduce the class of slice-polynomial functions: slice regular functions {defined over the quaternions, outside the real axis,} whose restriction to any c…
The Mittag-Leffler Theorem for regular functions of a quaternionic variable
Graziano Gentili, Giulia Sarfatti
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired…
A direct approach to quaternionic manifolds
Graziano Gentili, Anna Gori, Giulia Sarfatti
The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular man…
Quaternionic toric manifolds
Graziano Gentili, Anna Gori, Giulia Sarfatti
In the present paper we introduce and study a new notion of toric manifold in the quaternionic setting. We develop a construction with which, starting from appropriate -dimensio…
Ideals of regular functions of a quaternionic variable
Graziano Gentili, Giulia Sarfatti, Daniele C. Struppa
In this paper we prove that, for any , the ideal generated by slice regular functions having no common zeros concides with the entire ring of s…
Some Hilbert Spaces related with the Dirichlet space
Nicola Arcozzi, Karl-Mikael Perfekt, Pavel Mozolyako +2
We do a preliminary study of the reproducing kernel Hilbert space having as kernel , where is a positive integer and is the reproducing kernel of the analytic Dirichle…
The orthogonal projection on slice functions on the quaternionic sphere
Nicola Arcozzi, Giulia Sarfatti
We study the norm of the orthogonal projection from the space of quaternion valued functions to the closed subspace of slice functions.
Quaternionic Hankel operators and approximation by slice regular functions
Giulia Sarfatti
In this paper we study Hankel operators in the quaternionic setting. In particular we prove that they can be exploited to measure the distance of a slice …
From Hankel operators to Carleson measures in a quaternionic variable
Nicola Arcozzi, Giulia Sarfatti
We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari anc C. Fefferman are prove…
Landau-Toeplitz theorems for slice regular functions over quaternions
Graziano Gentili, Giulia Sarfatti
The theory of slice regular functions of a quaternionic variable extends the notion of holomorphic function to the quaternionic setting. This theory, already rich of results, is so…
A Bloch-Landau Theorem for slice regular functions
Chiara Della Rocchetta, Graziano Gentili, Giulia Sarfatti
The Bloch-Landau Theorem is one of the basic results in the geometric theory of holomorphic functions. It establishes that the image of the open unit disc under a holo…
The Bohr Theorem for slice regular functions
Chiara Della Rocchetta, Graziano Gentili, Giulia Sarfatti
In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Car…
Quaternionic Hardy spaces
Chiara de Fabritiis, Graziano Gentili, Giulia Sarfatti
The theory of slice regular functions of a quaternionic variable, introduced in 2006 by Gentili and Struppa, extends the notion of holomorphic function to the quaternionic setting.…
Invariant metrics for the quaternionic Hardy space
Nicola Arcozzi, Giulia Sarfatti
Riemannian metrics on the unit ball of the quaternions, which are naturally associated with the reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space…