64 citations · 426 across the 29 of their papers we have counts for
23 papers · 1 filter
On a continuation of quaternionic and octonionic logarithm along curves and the winding number
Graziano Gentili, Jasna Prezelj, Fabio Vlacci
This paper focuses on the problem of finding a continuous extension of the hypercomplex logarithm along a path. While a branch of the complex logarithm can be defined in a small op…
On a definition of logarithm of quaternionic functions
Graziano Gentili, Jasna Prezelj, Fabio Vlacci
For a slice--regular quaternionic function the classical exponential function is not slice--regular in general. An alternative definition of exponential function, the…
Slice conformality and Riemann manifolds on quaternions and octonions
Graziano Gentili, Jasna Prezelj, Fabio Vlacci
In this paper we establish quaternionic and octonionic analogs of the classical Riemann surfaces. The construction of these manifolds has nice peculiarities and the scrutiny of Ber…
A local representation formula for quaternionic slice regular functions
Graziano Gentili, Caterina Stoppato
After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motiv…
Zeros of slice functions and polynomials over dual quaternions
Graziano Gentili, Caterina Stoppato, Tomaso Trinci
This work studies the zeros of slice functions over the algebra of dual quaternions and it comprises applications to the problem of factorizing motion polynomials. The class of sli…
Minkowski products of unit quaternion sets
Rida T. Farouki, Graziano Gentili, Hwan Pyo Moon +1
The Minkowski product of unit quaternion sets is introduced and analyzed, motivated by the desire to characterize the overall variation of compounded spatial rotations that result…
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…
On Quaternionic Tori and their Moduli Spaces
Cinzia Bisi, Graziano Gentili
Quaternionic tori are defined as quotients of the skew field of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural stru…
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…
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…
Solution of a quadratic quaternion equation with mixed coefficients
Rida T. Farouki, Graziano Gentili, Carlotta Giannelli +2
A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construc…
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.…
The zero sets of slice regular functions and the open mapping theorem
G. Gentili, C. Stoppato
A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in recent years. Several results of the theory recall the classical…
Extension results for slice regular functions of a quaternionic variable
Fabrizio Colombo, Graziano Gentili, Irene Sabadini +1
In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function at a point can be recovered by…
A Cauchy kernel for slice regular functions
Fabrizio Colombo, Graziano Gentili, Irene Sabadini
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such fu…
Power series and analyticity over the quaternions
G. Gentili, C. Stoppato
We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of c…
A Phragmén - Lindelöf principle for slice regular functions
G. Gentili, C. Stoppato, D. C. Struppa
The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent…
Möbius transformations and the Poincaré distance in the quaternionic setting
Cinzia Bisi, Graziano Gentili
In the space $\hh$ of quaternions, we investigate the natural, invariant geometry of the open, unit disc $Δ_{\hh}$ and of the open half-space $\hh^{+}$. These two domains are diffe…
The open mapping theorem for regular quaternionic functions
G. Gentili, C. Stoppato
The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus…
Valiron's construction in higher dimension
Filippo Bracci, Graziano Gentili, Pietro Poggi-Corradini
We consider holomorphic self-maps $\v$ of the unit ball $\B^N$ in $\C^N$ (). In the one-dimensional case, when $\v$ has no fixed points in $\D\defeq \B^1$ and is of hy…