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The Leibniz Rule

In: Operator Relations Characterizing Derivatives

Author

Listed:
  • Hermann König

    (Universität Kiel, Mathematisches Seminar)

  • Vitali Milman

    (University of Tel Aviv, School of Mathematical Sciences)

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.

Suggested Citation

  • Hermann König & Vitali Milman, 2018. "The Leibniz Rule," Springer Books, in: Operator Relations Characterizing Derivatives, chapter 0, pages 29-52, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-00241-1_3
    DOI: 10.1007/978-3-030-00241-1_3
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