Related papers: Multipoint Schwarz-Pick Lemma for the quaternionic…
In their recent work, Gentili and Struppa proposed a different quaternionic analogue of the notion of holomorphic functions in the complex plane, called \textit{slice regular functions}, which has led to several analogues of classical…
We introduce Wirtinger operators for functions of several quaternionic variables. These operators are real linear partial differential operators which behave well on quaternionic polynomials, with properties analogous to the ones satisfied…
Many aspects of pluripotential theory are generalized to quaternionic $m$-subharmonic functions. We introduce quaternionic version of notions of the $m$-Hessian operator, $m$-subharmonic functions, $m$-Hessian measure, $m$-capapcity, the…
Due to the invalidation of the Gauss-Lucas type result for quaternionic polynomials, we first give in this paper an alternative proof of the Bernstein inequality in $L^{p} (1\leq p \leq+\infty)$ for slice regular polynomials by the Fej\'er…
We give simple proofs of various versions of the Schwarz lemma for real valued harmonic functions and for holomorphic (more generally harmonic quasi\-re\-gu\-lar, shortly HQR) mappings with the strip codomain. Along the way using the…
In this paper we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schrodinger-Maxwell system and to the nonlinear elliptic…
We investigate the Schwarz lemma and the Schur algorithm for elements in the unit ball of the multiplier algebra of a reproducing kernel Hilbert space on the open unit ball whose kernel satisfies the complete Nevanlinna-Pick property. This…
In this article, we introduce a new methodology to prove global parabolic Harnack inequalities on Riemannian manifolds. We focus on presenting a new proof of the global pointwise Harnack inequality satisfied by positive solutions of the…
A slice regular analogue of the Malmquist-Takenaka system is investigated. It is proved that they form a complete orthonormal system in the quaternionic Hardy spaces of the unit ball. The properties of associated projection operator are…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,\ldots, z_n\in \Omega$ and $w_1,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the $Pick\, interpolation\, problem$ asks when there is a…
The theory of slice regular functions of a quaternionic variable on the unit ball of the quaternions was introduced by Gentili and Struppa in 2006 and nowadays it is a well established function theory, especially in view of its applications…
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…
We study various aspects of Schur analysis in the slice hyperholomorphic setting. We present two sets of results: first, we give new results on the functional calculus for slice hyperholomorphic functions. In particular, we introduce and…
We develop an underlying relationship between the theory of rational approximations and that of isomonodromic deformations. We show that a certain duality in Hermite's two approximation problems for functions leads to the Schlesinger…
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part…
In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In…
Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between…
The aim of this article is to give an elementary proof of the fact that the Schwarz-Pick Lemma follows from the Ahlfors-Schwarz-Pick Lemma.
An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for…