2 papers
math.CA2026
Second-order derivations of function spaces -- a characterization of second-order differential operators
WÅodzimierz Fechner, Eszter Gselmann
Let be a nonempty and open set, then for all we have \begin{multline*} \diff{2}{x}(f\cdot g\cdot h) -f\diff{2}{x}(g\cdot h)-…
math.CA2025
A direct and algebraic characterization of higher-order differential operators
WÅodzimierz Fechner, Eszter Gselmann
This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extensio…