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For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.
In this paper, we study joint functional calculus for commuting $n$-tuple of Ritt operators. We provide an equivalent characterisation of boundedness for joint functional calculus for Ritt operators on $L^p$-spaces, $1< p<\infty$. We also…
Following the definitions of the algebras of differential operators, $\beta$-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free…
A classification of commutative integral domains consisting of ordinary differential operators with matrix coefficients is established in terms of morphisms between algebraic curves.
This paper explores the behaviour of commuting Jordan derivations over prime rings with non-trivial idempotents and demonstrates that they become zero maps. Further, it establishes this result for commuting Jordan higher derivations over…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
Recent innovations on the differential calculus for functions of non-commuting variables, begun for a quaternionic variable, are now extended to the case of a general matrix over the complex numbers. The expansion of F(X+Delta) is given to…
In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for them are proved.
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix…
A generic differential operator on the vectorial space of polynomial functions was presented in a recent work and applied in the study of differential relations fulfilled by polynomial sequences either orthogonal or 2-orthogonal. Using the…
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
We describe the closed, densely defined linear transformations commuting with a given operator T of class C_0 in terms of bounded operators in {T}'. Our results extend those of Sarason for operators with defect index 1, and Martin in the…
In this paper, we introduce and study a new concept of unbounded order demi Dunford-Pettis operators. Namely, we investigate some properties for this new class of operators and we study its connection with other known operators, we also…
In this paper we present commutativity results for a general class of Szasz-Mirakjan-Durrmeyer type operators and associated differential operators and investigate their eigenfunctions.