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math.CA2023
A characterization of differential operators in the ring of complex polynomials
Włodzimierz Fechner, Eszter Gselmann
The paper aims to provide a full characterization of all operators acting on the space of all complex polynomials that…
math.CA2023★ 1 cited
Characterizations of second-order differential operators
Włodzimierz Fechner, Eszter Gselmann, Aleksandra Świątczak
{Let be positive integers with , and be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ Δ(f\cdot g)(…
math.CA2023
Polynomial equations for additive functions II
Eszter Gselmann, Gergely Kiss
In this sequence of work we investigate polynomial equations of additive functions. We consider the solutions of equation \[ \sum_{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x)^{q_{i}}= 0 \qqua…