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Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
The properties of the Wilson rational functions ${}_{10}\phi_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a…
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
The q-Bessel-Macdonald functions of kinds 1, 2 and 3 are considered. Their representations by classical integral are constructed.
This paper is an introduction to the theory of multivector functions of a real variable. The notions of limit, continuity and derivative for these objects are given. The theory of multivector functions of a real variable, even being similar…
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.
An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…
We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems,…
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…
This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…
In this article, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral and derivative of order $\gamma = (p, q); p > 0,q >…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…