Related papers: Continuous Functional Calculus for Quaternionic Bo…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
This study utilizes Orlicz functions to provide refined lower and upper bounds on the q-numerical radius of an operator acting on a Hilbert space. Additionally, the concept of q-sectorial matrices is introduced and further bounds for the…
We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…
An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
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…
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
The papers \cite{O1,O2} are the first works to apply the theory of fiber bundles in the study of the quaternionic slice regular functions. The main goal of the present work is to extend the results given in \cite{O1}, where the quaternionic…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari anc C. Fefferman are proved.
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct…
We investigate the generalized quadratic operator defined by $$T =\left( \begin{array}{cc} a I_H & A \\ c A^* & bI_K \end{array} \right) ,$$ where $H$ and $K$ are Hilbert spaces, $A:K\to H$ is a bounded linear operator, $I_H$ and $I_K$…
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…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the…
We prove a continuous-parameter version of the recent theorem of Katznelson-Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We also show that the result can be extended to some operators…