Related papers: Construction of the generalised q-derivative opera…
By a generalized Delsarte polynomial we mean a Laurent polynomial whose exponent vectors are linearly independent. We consider certain monomial deformations of generalized Delsarte polynomials and study their associated differential…
The properties of the Pastro polynomials on the real line are studied with the help of a triplet of $q$-difference operators. The $q$-difference equation and recurrence relation these polynomials obey are shown to arise as generalized…
We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace…
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
Using the theory of functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, then, it can be expanded in terms of the product of the…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
The cyclic group labeled family of quasi-projection operators is used for investigation of decomposition of functions with respect to the cyclic group of order n . Series of new identities thus arising are demonstrated and new perspectives…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…
On conformal manifolds of even dimension $n\geq 4$ we construct a family of new conformally invariant differential complexes. Each bundle in each of these complexes appears either in the de Rham complex or in its dual. Each of the new…
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 consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald-Ruijsenaars operator in infinite number of variables. The ideals of these varieties are…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
In this paper, at first the construction of Lie higher derivations and higher derivations on a generalized matrix algebra were characterized; then the conditions under which a Lie higher derivation on generalized matrix algebras is proper…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…