Related papers: Fractional slice regular functions of a quaternion…
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 functions, which leads to a new Cauchy formula. We find the…
Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…
In this paper we introduce fractional powers of quaternionic operators. Their definition is based on the theory of slice-hyperholomorphic functions and on the $S$-resolvent operators of the quaternionic functional calculus. The integral…
Slice regular functions have been extensively studied over the past decade, but much less is known about their boundary behavior. In this paper, we initiate the study of Julia theory for slice regular functions. More specifically, we…
Along with the development of the theory of slice regular functions over the real algebra of quaternions $\mathbb{H}$ during the last decade, some natural questions arose about slice regular functions on the open unit ball $\mathbb{B}$ in…
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 sometimes surprisingly different from the theory of…
The purpose of this paper is twofold. One is to enrich from a geometrical point of view the theory of octonionic slice regular functions. We first prove a boundary Schwarz lemma for slice regular self-mappings of the open unit ball of the…
We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as…
We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated with the concept of slice-regularity and to the spherical Dirac operator. These…
In this paper we propose an Almansi-type decomposition for slice regular functions of several quaternionic variables. Our method yields $2^n$ distinct and unique decompositions for any slice function with domain in $\mathbb{H}^n$. Depending…
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 and Clifford algebras. This theory is an extension of the…
We prove a Cauchy-type integral formula for slice-regular functions where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry. In particular, we get a local…
The theory of slice regular functions is nowadays widely studied and has found its elegant applications to a functional calculus for quaternionic linear operators and Schur analysis. However, much less is known about their boundary…
Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice…
Notions of a "holomorphic" function theory for functions of a split-quaternionic variable have been of recent interest. We describe two found in the literature and show that one notion encompasses a small class of functions, while the other…
In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function $f$ at a point $q=x+yI$ can be recovered by the values of $f$ at the points $q+yJ$ and $q+yK$ for any…
The quaternionic valued functions of a quaternionic variable, often referred to as slice regular functions has been studied extensively due to the large number of generali\-zed results of the theory of one complex variable, see…
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 manifold, as a space locally modeled on $\mathbb{H}^n$, in a…
This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann-Liouville and Caputo definitions, we discuss when the fractional derivative and when…
This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator…