Related papers: Generalized Discrete Operators
We define new generalizations of (q,t)-Catalan numbers applying nabla operator on k-Schur functions indexed by column partitions. In some special cases, we give a combinatorial interpretation of these numbers using configurations of Dyck…
In this paper we determine the number of the meaningful compositions of higher order of the differential operations and Gateaux directional derivative.
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform and tridendriform algebra. We show that several types of…
The concept of $\lambda$-differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the $\lambda$-differential Lie algebraic structure on the Witt algebra and the…
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…
The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
This paper presents some properties and applications of "transversal operators". Two transversal operators are presented: a "translation" operator T and a "dilation" operator D. Such operators are used in common analysis systems including…
We give estimates on discrete fractional integral operators along binary quadratic forms. These operators have been studied for 30 years starting with the investigations of Arkhipov and Oskolkov, but efforts have concentrated on cases where…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
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 define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
We Investigate two types of dual identities for Riemann fractional sums and differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
We extend the De Giorgi-Nash-Moser theory to nonlocal, possibly degenerate integro-differential operators.
There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of…
Ordinary and partial differential equation for unknown functions defined on the Cantor dyadic group are studied. We consider two types of equations: related to the Gibbs derivatives and to the fractional modified Gibbs derivatives (or…