2025/04/14 by Fechner, Włodzimierz, Gselmann, Eszter
#39B22 #47A62 #47B38 #47B92 #47J05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.10100
This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extension to higher orders typically involves identities relating multiple distinct operators. In contrast, we introduce a novel operator equation involving only a single n\textsuperscriptth-order differential operator. We demonstrate that, under certain mild conditions, this equation serves to characterize such operators. Specifically, our results show that these higher-order differential operators can be identified as particular solutions to this single-operator identity. This approach provides a framework for understanding the algebraic structure of higher-order differential operators acting on function spaces.