Related papers: On Some Geometric Properties of Slice Regular Func…
Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class…
In this paper we generalize the classical theorems of Brown and Halmos about algebraic properties of Toeplitz operators to Bergman spaces over the unit ball in several complex variables. A key result, which is of independent interest, is…
In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functions. We first study the axial symmetry and monotonicity of…
We study the relations between the quaternion $H$-type group and the boundary of the unit ball on two dimensional quaternionic space. The orthogonal projection of the space of square integrable functions defined on quaternion $H$-type group…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…
For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a…
In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see \cite{gs}, and the key tools are a new resolvent operator and a new…
We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…
We give a complete description of the possible ranges of real Smirnov functions (quotients of two bounded analytic functions on the open unit disk where the denominator is outer and such that the radial boundary values are real almost…
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
The aim of this paper is to study some features of slice semi-regular functions $\mathcal{RM}(\Omega)$ on a circular domain $\Omega$ contained in the skew-symmetric algebra of quaternions $\mathbb{H}$ via the analysis of a family of linear…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
In this paper we study octonion regular functions and the structural differences between regular functions in octonion, quaternion, and Clifford analyses.
In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general low-degree functions, with no constraints on the influences.…
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii…
A lot of attention has been drawn over the last few years by the investigation of the geometry of spherical random eigenfunctions (random spherical harmonics) in the high frequency regime, i.e ., for diverging eigenvalues. In this paper, we…
The theory of slice regular functions over the quaternions, introduced by Gentili and Struppa in [5], was born on domains that intersect the real axis. This hypothesis can be overcome using the theory of stem functions introduced by Ghiloni…
In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…