Related papers: Quaternionic Fock space in an Euclidean unit ball …

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable…

A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of…

In this paper, we study a specific system of Clifford-Appell polynomials and in particular their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions.…

We construct new examples of embedded, complete minimal hypersurfaces in quaternionc hyperbolic space and also some minimal foliations. We introduce fans an construct analytic deformations of bisectors.

We prove that if $C$ is a symmetric convex body of revolution in $\mathbb R^4$ containing the unit Euclidean ball $\mathbb B_4$, such that the sections of $C$ by hyperplanes tangent to $\mathbb B_4$ have constant area $A>0$, then $C$ is a…

We consider the sampling problem for two-sided small Fock spaces $\mathcal{F}^p_{\alpha}$, for the full range $0 < p \le \infty$. We establish a geometric description of shift-invariant sampling sequences, i.e., sequences $\Lambda$ such…

The authors obtained the classification theorem for Lagrangian H-umbilical submanifolds in quaternion Euclidean spaces using the idea of quaternion extensors.

This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…

We introduce two classes of right quaternionic Hilbert spaces in the context of slice polyregular functions, generalizing the so-called slice and full hyperholomorphic Bargmann spaces. Their basic properties are discussed, the explicit…

In this paper we provide a general construction of a quaternionic Banach space of slice regular functions from a given Banach space of holomorphic functions, which we call its quaternionic lift. To the best of our knowledge, this…

Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit…

We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A affine Lie…

Several sets of quaternionic functions are described and studied with respect to hy-perholomorphy, addition and (non commutative) multiplication, on open sets of H, then Hamil-ton 4-manifolds analogous to Riemann surfaces, for H instead of…

Explicit formulas are obtained for a family of continuous mappings of p-adic numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space \~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for which…

Here we follow the basic analysis that is common for real and complex variables and find how it can be applied to a quaternionic variable. Non-commutativity of the quaternion algebra poses obstacles for the usual manipulations; but we show…

The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…

Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic…

In this article we give an introduction to the Fock quantization of the Maxwell field. At the classical level, we treat the theory in both the covariant and canonical phase space formalisms. The approach is general since we consider…

We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…

Let $\mathcal{M}(n,m;\F \bp^n)$ be the configuration space of $m$-tuples of pairwise distinct points in $\F \bp^n$, that is, the quotient of the set of $m$-tuples of pairwise distinct points in $\F \bp^n$ with respect to the diagonal action…