234 citations · 697 across the 29 of their papers we have counts for
33 papers
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.…
The Nash-Tognoli theorem over the rationals and its version for isolated singularities
Riccardo Ghiloni, Enrico Savi
Let be the field of rational numbers and let be a subset of . We say that is -algebraic if it is the common zero set in $\mathbb{R}^n…
The curved Mimetic Finite Difference method: allowing grids with curved faces
Silvano Pitassi, Riccardo Ghiloni, Igor Petretti +2
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric disc…
Inverting the discrete curl operator: a novel graph algorithm to find a vector potential of a given vector field
Silvano Pitassi, Riccardo Ghiloni, Ruben Specogna
We provide a novel framework to compute a discrete vector potential of a given discrete vector field on arbitrary polyhedral meshes. The framework exploits the concept of acyclic m…
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…
On the generators of Clifford semigroups: polynomial resolvents and their integral transforms
Riccardo Ghiloni, Vincenzo Recupero
This paper deals with generators of strongly continuous right linear semigroups in Banach two-sided spaces whose set of scalars is an arbitrary Clifford algebra $\math…
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…
Efficient computation of Linking number with certification
Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the result…
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…
Differentiable approximation of continuous semialgebraic maps
José F. Fernando, Riccardo Ghiloni
In this work we approach the problem of approximating uniformly continuous semialgebraic maps from a compact semialgebraic set to an arbitrary semialgebraic set …
Smooth approximations in PL geometry
José F. Fernando, Riccardo Ghiloni
Let be a triangulable set and let be either a positive integer or . We say that is a -approximation target space, or a $\ma…
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…
Algebraicity of Nash sets and of their asymmetric cobordism
Riccardo Ghiloni, Alessandro Tancredi
This paper deals with the existence of algebraic structures on compact Nash sets. We introduce the algebraic-topological notion of asymmetric Nash cobordism between compact Nash se…
Towards Fulton's conjecture
Claudio Fontanari, Riccardo Ghiloni, Paolo Lella
We present an alternate proof, much quicker and more straightforward than the original one, of a celebrated Fulton's conjecture on the ample cone of the moduli space of stable rati…
Geometric construction of bases of
Ana Alonso Rodríguez, Enrico Bertolazzi, Riccardo Ghiloni +1
We present an efficient algorithm for the construction of a basis of via the Poincaré--Lefschetz duality theorem. Denoting by the first Be…
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…
Slice regular semigroups
Riccardo Ghiloni, Vincenzo Recupero
In this paper we introduce the notion of slice regular right linear semigroup in a quaternionic Banach space. It is an operatorial function which is slice regular (a noncommutative…
Spectral representations of normal operators via Intertwining Quaternionic Projection Valued Measures
Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann's foundational works in the thirties. The absence of a suitable…
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…
Efficient construction of homological Seifert surfaces
Ana Alonso Rodrìguez, Enrico Bertolazzi, Riccardo Ghiloni +1
Let be a bounded domain of whose closure is polyhedral, and let be a triangulation of . Assuming that the boundary of …
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…