Zobrazeno 1 - 10
of 173
pro vyhledávání: '"Ghiloni, Riccardo"'
Autor:
Ghiloni, Riccardo, Stoppato, Caterina
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises Fueter-regular functio
Externí odkaz:
http://arxiv.org/abs/2408.01523
Autor:
Ghiloni, Riccardo, Recupero, Vincenzo
In the present paper, we prove a resolvent equation for the $\mathcal{S}$-resolvent operator in the quaternionic framework. Exploiting this resolvent equation, we find a series expansion for the $\mathcal{S}$-resolvent operator in an open neighborhoo
Externí odkaz:
http://arxiv.org/abs/2402.00511
Autor:
Ghiloni, Riccardo, Stoppato, Caterina
Publikováno v:
Math. Z., 306(3):55 (2024)
After Gentili and Struppa introduced in 2006 the theory of quaternionic slice regular function, the theory has focused on functions on the so-called slice domains. The present work defines the class of speared domains, which is a rather broad extensi
Externí odkaz:
http://arxiv.org/abs/2312.13982
Autor:
Ghiloni, Riccardo, Stoppato, Caterina
Publikováno v:
J. Geom. Phys., 202:105219 (2024)
We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternion
Externí odkaz:
http://arxiv.org/abs/2309.02891
Autor:
Ghiloni, Riccardo, Savi, Enrico
We prove that every real algebraic set $V\subset\mathbb{R}^n$ with isolated singularities is homeomorphic to a set $V'\subset\mathbb{R}^m$ that is $\mathbb{Q}$-algebraic in the sense that $V'$ is defined in $\mathbb{R}^m$ by polynomial equations with
Externí odkaz:
http://arxiv.org/abs/2302.04142
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 discrete problem that uses only one discrete unknown per curved face. The
Externí odkaz:
http://arxiv.org/abs/2203.13105
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 matching, a combinatorial tool at the core of discrete Morse theory. We
Externí odkaz:
http://arxiv.org/abs/2111.04431
Publikováno v:
J. Noncommut. Geom., 16(2): 637--676 (2022)
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 octonionic slice regular functions. Moreover, it opens the path for a poss
Externí odkaz:
http://arxiv.org/abs/2109.12902
Autor:
Ghiloni, Riccardo, Stoppato, Caterina
Publikováno v:
In Journal of Geometry and Physics August 2024 202
Autor:
Ghiloni, Riccardo, Recupero, Vincenzo
This paper deals with generators $\mathsf{A}$ of strongly continuous right linear semigroups in Banach two-sided spaces whose set of scalars is an arbitrary Clifford algebra $\mathit{C}\ell(0,n)$. We study the invertibility of operators of the form $
Externí odkaz:
http://arxiv.org/abs/2104.07110