The Leibniz Rule

Hermann König and Vitali Milman
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Hermann König: Universität Kiel, Mathematisches Seminar
Vitali Milman: University of Tel Aviv, School of Mathematical Sciences

Chapter Chapter 3 in Operator Relations Characterizing Derivatives, 2018, pp 29-52 from Springer

Abstract: Abstract We will show that the derivative as a map on classical function spaces of analysis is characterized by the Leibniz rule as well as the chain rule. This is a consequence of results in this and the next chapter. We first study the solutions of the Leibniz rule equation as a map on the k-times continuously differentiable functions Ck. There are many examples of derivations in algebra and differential geometry generalizing the Leibniz rule for the derivative of products of functions.

Date: 2018
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DOI: 10.1007/978-3-030-00241-1_3

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