Related papers: Bicomplex algebra and function theory

For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…

We consider a manifestly Lorentz invariant form $\mathbb L$ of the biquaternion algebra and its generalization to the case of curved manifold. The conditions of $\mathbb L$-differentiability of $\mathbb L$-functions are formulated and…

The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…

In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a…

Motivated by the integral representation of the Euler Beta function, we introduce its Cauchy siblings and investigate some of their properties. Two of these newly introduced functions happen to coincide with some classical means, such as…

The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…

The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…

In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

In this article we provide a generalized version of the result of L.H. Son and W. Tutschke \cite{tut} on the solvability of first order systems on the plane whose initial functions are arbitrary holomorphic functions. This is achieved by…

This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…

The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be…

Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…

The $S$-functional calculus for slice hyperholomorphic functions generalizes the Riesz-Dunford-functional calculus for holomorphic functions to quaternionic linear operators and to $n$-tuples of noncommuting operators. For an unbounded…

The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…

In this article we use the expansion for biquantization described in Cattaneo-Felder [math.QA/0309180] for the case of symmetric spaces. We introduce a function of two variables $E(X,Y)$ for any symmetric pairs. This function has an…