Related papers: Difference-differential fields of continuous funct…
In this paper, among other things, we prove that any subset of $\overline{\mathbb{Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountable many transcendental entire functions over…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution…
We propose and develop a new calculus for local variational differential operators. The main difference of the new formalism with the canonical differential calculus is that the image of higher order operators on local functionals does not…
For any positive integers $n$ and $m$, $\mathbb{H}_{n,m}:=\mathbb{H}_n\times\mathbb{C}^{(m,n)}$ is called the Siegel-Jacobi space, with the Jacobi group acting on it. The Jacobi forms are defined on this space. In this article we compute…
The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most…
Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…
Radul has recently introduced a map from the Lie algebra of differential operators on the circle to $W_n$. In this note we extend this map to $W_{KP}^{(q)}$, a recently introduced one-parameter deformation of $W_{KP}$---the second…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
In the paper under review, we construct complex powers of multivalued linear operators with polynomially bounded $C$-resolvent existing on an appropriate region of the complex plane containing the interval $(-\infty,0].$ In our approach,…
We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition,…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
In this paper we investigate the modulus of continuity of differential operator of order $k$, $k\in\mathbb{N}$, on the classes of functions defined on half-line that have positive non-increasing continuous majorants of functions and their…
We give explicit $q$-difference operators acting diagonally on wreath Macdonald $P$-polynomials in finitely many variables.
By applying the derivative operator to the corresponding hypergeometric form of a $q$-series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number identity. As the special cases of it, several interesting…
In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion formula, and simple integrals, integral operators, some…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…