• Corpus ID: 238215406

On the Quadratic Cone of $\mathbb{R}_3.$

  title={On the Quadratic Cone of \$\mathbb\{R\}\_3.\$},
  author={Cinzia Bisi and Antonino De Martino},
In this paper we study the following type of functions f : QR3 → R3, where QR3 is the quadratic cone of the algebra R3. From the fact that it is possible to write the algebra R3 as a direct sum of quaternions, we get the observation that it is possible to find a clever representation for QR3 . By using this result a slice regular theory was introduced and a Cauchy formula is discussed. Moreover, a detailed study of the zeros is performed. Finally, we find a formula for the determinant of a… 



On Brolin's theorem over the quaternions

In this paper we investigate the Brolin's theorem over $\mathbb{H}$, the skew field of quaternions. Moreover, considering a quaternionic polynomial $p$ with real coefficients, we focus on the

Landau’s theorem for slice regular functions on the quaternionic unit ball

During the development of the theory of slice regular functions over the real algebra of quaternions ℍ in the last decade, some natural questions arose about slice regular functions on the open unit

Log-biharmonicity and a Jensen formula in the space of quaternions

Given a complex meromorphic function, it is well defined its Riesz measure in terms of the laplacian of the logarithm of its modulus. Moreover, related to this tool, it is possible to prove the

The algebra of slice functions

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

The Schwarz-Pick lemma for slice regular functions

The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to

Poles of regular quaternionic functions

This article studies the singularities of functions of one quaternionic variable which are regular in the sense of Gentili and Struppa (A new theory of regular functions of a quaternionic variable,

Power and spherical series over real alternative *-algebras

We study two types of series over a real alternative $^*$-algebra $A$. The first type are series of the form $\sum_{n} (x-y)^{\punto n}a_n$, where $a_n$ and $y$ belong to $A$ and $(x-y)^{\punto n}$

On quaternionic tori and their moduli space

Quaternionic tori are defined as quotients of the skew field $\mathbb{H}$ of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural structures of