Related papers: Differential and linear integral operators represe…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ and differential operators $L_1$ and $L_{2}$, that has implications for spectral properties of $K$. This…
In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability…
Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
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…
Several definitions of differential operators on modules over noncommutative rings are discussed.
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
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 study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
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…
In this paper we give the answers to two open questions on complex symmetric composition operators. By doing this, we give a complete description of complex symmetric composition operators whose symbols are linear fractional.
We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.