arXiv subjects

Giulio Binosi

Publications and source records attributed to Giulio Binosi.

6 recordsLinked to original sources

arXiv2026

Dunkl regularity over alternative $*$-algebras

We characterise slice-regularity of functions over a real alternative *-algebra using operators that arise in Dunkl operator theory. We present a unifying perspective on hypercomplex analysis by defining a family of function spaces in the kernel of Dunkl-Cauchy-Riemann operators. Each of these function spaces, whose elements are called Dunkl-regular functions, refines Dunkl monogenic function theory and Dunkl harmonic analysis on Euclidean spaces. This approach allows a wide variety of hypercomplex function theories to be embedded as subcases of Dunkl monogenic function theory. This paves the way for further interactions between Dunkl theory and hypercomplex analysis.

math.CV↗

arXiv2026

Dunkl approach to slice regular functions

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 Dunkl-spherical Dirac operator and that a slice function is slice regular if, and only if, it lies in the kernel of the Dunkl-Cauchy-Riemann operator for a suitable parameter. Based on this correspondence and the inverse Dunkl intertwining operator, we propose a new method to construct a family of classical monogenic functions from a given holomorphic function, in the spirit of Fueter theorem.

math.CV↗

arXiv2025

Slice regular holomorphic Cliffordian functions of order $k$

Holomorphic Cliffordian functions of order $k$ are functions in the kernel of the differential operator $\overline{\partial}Δ^k$. When $\overline{\partial}Δ^k$ is applied to functions defined on the paravector space of some Clifford Algebra $\mathbb{R}_m$ with an odd number of imaginary units, the Fueter-Sce construction establish a critical index $k=\frac{m-1}{2}$ (sometimes called Fueter-Sce exponent) for which the class of slice regular functions is contained in the one of holomorphic Cliffordian functions of order $\frac{m-1}{2}$. In this paper we analyze the case $k<\frac{m-1}{2}$ and we find that the polynomials of degree at most $2k$ are the only slice regular holomorphic Cliffordian functions of order $k$.

math.CV↗

arXiv2025

Polyharmonicity, Almansi-type decompositions and Fueter-Sce theorem for several Clifford variables

We study some harmonic properties of slice regular functions in one and several Clifford variables and give explicit formulas of the iterated Laplacian applied to slice regular functions and to their spherical derivative, which are new also in the one variable context. We propose several Almansi-type decompositions for slice functions in several Clifford variables. As a consequence, we establish a several variables version of Fueter-Sce theorem.

math.CV↗

arXiv2024

Almansi-type decomposition for slice regular functions of several quaternionic variables

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 on the choice of the decomposition, every component is given explicitly, uniquely determined and exhibits desirable properties, such as harmonicity and circularity in the selected variables. As consequences of these decompositions, we give another proof of Fueter's Theorem in $\mathbb{H}^n$, establish the biharmonicity of slice regular functions in every variable and derive mean value and Poisson formulas for them.

math.CV↗

arXiv2024

Partial slice regularity and Fueter's Theorem in several quaternionic variables

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 characterized. We introduce new notions of partial spherical value and derivative for functions of several variables that extend those of one variable. We recover some of their properties as circularity, harmonicity, some relations with differential operators and a Leibniz rule w.r.t. the slice product as well as studying their behavior in the context of several variables. Then, we prove our main result, which is a generalization of Fueter's Theorem for slice regular functions in several variables. This extends the link between slice regular and axially monogenic functions well known in the one variable context.

math.CV↗