Related papers: Classifying Slice-Regular Polynomials via Group Ac…

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 complex half-plane is a polynomial. These functions naturally…

The concept of slice regular function over the real algebra $\mathbb{H}$ of quaternions is a generalization of the notion of holomorphic function of a complex variable. Let $\Omega$ be an open subset of $\mathbb{H}$, which intersects…

Given a slice regular function $f:\Omega\subset\mathbb{H}\to \mathbb{H}$, with $\Omega\cap\mathbb{R}\neq \emptyset$, it is possible to lift it to a surface in the twistor space $\mathbb{CP}^{3}$ of $\mathbb{S}^4\simeq \mathbb{H}\cup…

The aim of this paper is to study some features of slice semi-regular functions $\mathcal{RM}(\Omega)$ on a circular domain $\Omega$ contained in the skew-symmetric algebra of quaternions $\mathbb{H}$ via the analysis of a family of linear…

Slice Fueter-regular functions, originally called slice Dirac-regular functions, are generalized holomorphic functions defined over the octonion algebra $\mathbb{O}$, recently introduced by M. Jin, G. Ren and I. Sabadini. A function…

Slice regular functions are a generalization of holomorphic functions to the setting of quaternions (and more generally, Clifford algebras). In this paper, we first establish the Bohr inequality for slice starlike functions and slice…

In this article we investigate harmonicity, Laplacians, mean value theorems and related topics in the context of quaternionic analysis. We observe that a Mean Value Formula for slice regular functions holds true and it is a consequence of…

The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains \Omega\ of R^4. When \Omega\ is a symmetric slice domain, the twistor transform of such a function is a…

Holomorphic Cliffordian functions of order $k$ are functions in the kernel of the differential operator $\overline{\partial}\Delta^k$. When $\overline{\partial}\Delta^k$ is applied to functions defined on the paravector space of some…

We introduce two classes of right quaternionic Hilbert spaces in the context of slice polyregular functions, generalizing the so-called slice and full hyperholomorphic Bargmann spaces. Their basic properties are discussed, the explicit…

We present some new relations between the Cauchy-Riemann operator on the real Clifford algebra $\mathbb R_n$ of signature $(0,n)$ and slice-regular functions on $\mathbb R_n$. The class of slice-regular functions, which comprises all…

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…

Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between…

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which…

In this paper, we establish a connection between Dunkl analysis and slice analysis in the setting of Clifford algebras. Specifically, we show that a Clifford algebra-valued function is slice if, and only if, it belongs to the kernel of the…

In this paper we develop a theory of slice regular functions on a real alternative algebra $A$. Our approach is based on a well--known Fueter's construction. Two recent function theories can be included in our general theory: the one of…

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…

In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize…

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…

Let $A$ be one of the following Clifford algebras : $\mathbb{R}_2 \cong \mathbb{H}$ or $\mathbb{R}_3$. For the algebra $A$, the automorphism group $Aut(A)$ and its invariants are well known. In this paper we will describe the invariants of…