Related papers: A New Definition of Hypercomplex Analyticity

In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…

We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…

In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.

We propose definitions of hypercomplex analytic spaces and hypercomplex schemes. We show that such a hypercomplex space is canonically associated to the quotient of a hypercomplex manifold by a finite group action.

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…

We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of convergence (which is a ball B(0,R) centered at 0). At each…

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…

We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…

The main properties of hypercomplex generalization of quaternion system as antiquaternion are presented in this article. Definitions and studied of antiquaternions conjugation are introduced, their norm and zero divisor, and how to perform…

The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…

Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…

Due to the noncommutative nature of quaternions and octonions we introduce barred operators. This objects give the opportunity to manipulate appropriately the hypercomplex fields. The standard problems arising in the definitions of…

Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction…

The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…

Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…

We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…

This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…

Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and generalizes to higher dimension the theory of holomorphic functions in the complex plane.…

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…

We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over…