Related papers: Some properties for quaternionic slice-regular fun…
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…
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 unexpected phenomena are discovered. The results are applied to…
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 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…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
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…
In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the…
The aim of this paper is to prove that a large class of quaternionic slice regular functions result to be (ramified) covering maps. By means of the topological implications of this fact and by providing further topological structures, we…
Octonionic analysis is becoming eminent due to the role of octonions in the theory of G2 manifold. In this article, a new slice theory is introduced as a generalization of the holomorphic theory of several complex variables to the…
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…
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…
We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…
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…
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…
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…
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…
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…
The theory of slice regular (also called hyperholomorphic) functions is a generalization of complex analysis originally given in the quaternionic framework, and then further extended to Clifford algebras, octonions, and to real alternative…
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…
This paper extends the $*$-product from slice analysis to weakly slice analysis in several quaternionic variables, focusing on non-axially symmetric domains. It diverges from traditional applications in axially symmetric domains to address…