Related papers: Representation of Quaternionic $\psi$-hyperholomor…
Superoscillatory functions represent a counterintuitive phenomenon in physics but also in mathematics, where a band-limited function oscillates faster than its highest Fourier component. They appear in various contexts, including quantum…
In the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford algebras to non-associative Cayley-Dickson algebras, starting with the octonions. An important…
A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion…
Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
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…
We introduce the notion of characteristic function of a quaternionic matrix, whose roots are the left eigenvalues. We prove that for all $2\times 2$ matrices and for $3\times 3$ matrices having some zero entry outside the diagonal there is…
We introduce a new family of special functions, namely $q$-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to $q$-analogues of Poisson distributions. We focus our attention on their structural…
In this paper I explore the set of quaternion algebras over field. Quaternion algebra E(C,-1,-1) is isomorphic to tensor product of complex field C and quaternion algebra H=E(R,-1,-1). Considered two sets of quaternion functions, which…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
This paper introduce a fractional-fractal $\psi$-Fueter operator in the quaternionic context inspired in the concepts of proportional fractional derivative and Hausdorff derivative of a function with respect to a fractal measure. Moreover,…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
In this paper we introduce and study some basic properties of the Fock space (also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We discuss both the case of slice regular functions over quaternions and also the case…
This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the Hunter-Saxton (HS) hierarchy through studying a algebro-geometric initial value problem. Our main tools…
The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere…
The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…
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…
Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the S-spectrum has applications, for example, in the formulation…
We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric…