Related papers: On calculus with a quaternionic variable and its c…
We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as…
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…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.
Notions of a "holomorphic" function theory for functions of a split-quaternionic variable have been of recent interest. We describe two found in the literature and show that one notion encompasses a small class of functions, while the other…
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…
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…
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…
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding…
We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free…
Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…
We define an almost periodic extension of the Wiener algebras in the quaternionic setting and prove a Wiener-Levy type theorem for it, as well as extending the theorem to the matrix-valued case. We prove a Wiener-Hopf factorization theorem…
The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular…
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…
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of…
The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of…
In this paper, several differentiability criteria for real functions of multiple variables in n-dimensional Euclidean space are considered. Simple and easy-to-use Cauchy-like criterion is formulated and proven. Relaxed sufficient conditions…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
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…