Definition:Distributional Derivative/Higher Derivatives
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Definition
The $n$th distributional derivative of a distribution $T \in \map \DD \R$ is defined as:
- $T^{\paren n} := \begin {cases}
\paren {T^{\paren {n - 1}}}' & : n > 0 \\ T & : n = 0 \end {cases}$
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 6.2$: A glimpse of distribution theory. Derivatives in the distributional sense