Related papers: Slice regular functions in several variables

We prove a Slice Theorem around closed leaves in a singular Riemannian foliation, and we use it to study the $C^\infty$-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G.~Schwarz. In…

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…

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 extend the $H^\infty$ functional calculus to quaternionic operators and to $n$-tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus, called…

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…

Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the S-spectrum has applications, for example, in the formulation…

This paper is concerned with a class of generalized slice Fueter-regular functions on arbitrary domains in O with local stem functions. Some classical theorems such as the maximum modulus principle will be generalized to our setting. Some…

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…

Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…

This work studies the zeros of slice functions over the algebra of dual quaternions and it comprises applications to the problem of factorizing motion polynomials. The class of slice functions over an alternative $*$-algebra $A$ was defined…

In this paper we prove two Bloch type theorems for quaternionic slice regular functions. We first discuss the injective and covering properties of some classes of slice regular functions from slice regular Bloch spaces and slice regular…

In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$…

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.

In this paper, we are concerned with the S-polyregularity the regular dot product of slice regular functions. We prove that the product of a slice regular function and right quaternionic polynomial function is a S-polyregular function and…

According to [5] we define the $*$-exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for $\exp_*(f)$ are provided, also in terms of suitable sine and…

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…

In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

In the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford algebras to non-associative Cayley-Dickson algebras, starting with the octonions. An important…

We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice…