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math.CA2025
A direct and algebraic characterization of higher-order differential operators
Włodzimierz 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…
math.CA2025
Second-order derivations of function spaces -- a characterization of second-order differential operators
Włodzimierz 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)-g\…