Related papers: On quaternionic functions
The functions studied in the paper are quaternion-valued functions of a quaternionic variable. It is show that the left slice regular functions and right slice regular functions are related by a particular involution. The relation between…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non commutative) multiplication, on open sets of $\mathbb H$. The aim is to get a local function theory.
We study properties of inner and outer functions in the Hardy space of the quaternionic unit ball. In particular, we give sufficient conditions as well as necessary ones for functions to be inner or outer.
Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.
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…
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…
This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The…
Due to the non-commutative nature of quaternions we introduce the concept of left and right action for quaternionic numbers. This gives the opportunity to manipulate appropriately the $H$-field. The standard problems arising in the…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
In this paper we shall study the inverse problem relative to dynamics of the w function which is a special arithmetic function and shall get some results.
In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.
The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…
In this paper we study octonion regular functions and the structural differences between regular functions in octonion, quaternion, and Clifford analyses.
We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to…