234 citations · 697 across the 29 of their papers we have counts for
16 papers · 1 filter
Reconstruction of a slice regular function from some of its real components
Cinzia Bisi, Antonio Carbone, Riccardo Ghiloni
A basic property of holomorphic functions defined on domains of is that is uniquely determined by its real part up to an additive constant.…
Slice regular functions and orthogonal complex structures over
Riccardo Ghiloni, Alessandro Perotti, Caterina Stoppato
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octo…
Slice-by-slice and global smoothness of slice regular and polyanalytic functions
Riccardo Ghiloni
The concept of slice regular function over the real algebra of quaternions is a generalization of the notion of holomorphic function of a complex variable. Let be…
Slice regular functions in several variables
Riccardo Ghiloni, Alessandro Perotti
In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative -algebra, including quaternions, octonions a…
Slice Fueter-regular functions
Riccardo Ghiloni
Slice Fueter-regular functions, originally called slice Dirac-regular functions, are generalized holomorphic functions defined over the octonion algebra , recently intr…
On a class of orientation-preserving maps of
Riccardo Ghiloni, Alessandro Perotti
The purpose of this paper is to present several new, sometimes surprising, results concerning a class of hyperholomorphic functions over quaternions, the so-called slice regular fu…
The quaternionic Gauss-Lucas Theorem
Riccardo Ghiloni, Alessandro Perotti
The classic Gauss-Lucas Theorem for complex polynomials of degree has a natural reformulation over quaternions, obtained via rotation around the real axis. We prove that su…
Division algebras of slice functions
Riccardo Ghiloni, Alessandro Perotti, Caterina Stoppato
This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpect…
Singularities of slice regular functions over real alternative *-algebras
Riccardo Ghiloni, Alessandro Perotti, Caterina Stoppato
The main goal of this work is classifying the singularities of slice regular functions over a real alternative *-algebra A. This function theory has been introduced in 2011 as a hi…
The algebra of slice functions
Riccardo Ghiloni, Alessandro Perotti, Caterina Stoppato
In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative -algebra over . These recently i…
Noncommutative Cauchy integral formula
Riccardo Ghiloni, Alessandro Perotti, Vincenzo Recupero
The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regu…
Lagrange polynomials over Clifford numbers
Riccardo Ghiloni, Alessandro Perotti
We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions , or to the real Clifford algebra $R_{0…
Power and spherical series over real alternative *-algebras
Riccardo Ghiloni, Alessandro Perotti
We study two types of series over a real alternative -algebra . The first type are series of the form $\sum_{n} (x-y)^{\punto n}a_n$, where and belong to and $…
Volume Cauchy formulas for slice functions on real associative *-algebras
Riccardo Ghiloni, Alessandro Perotti
We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the a…
Slice regular functions on real alternative algebras
Riccardo Ghiloni, Alessandro Perotti
In this paper we develop a theory of slice regular functions on a real alternative algebra . Our approach is based on a well--known Fueter's construction. Two recent function th…
Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect
Riccardo Ghiloni, Alessandro Perotti
We study in detail the zero set of a regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation…