Definition:Distribution/Notation

Distribution: Notation

To avoid confusion between a distribution and the generating function involved, one can write the function as a subscript.

Suppose we have a distribution $T_f : \map \DD \R \to \C$ and a test function $\phi \in \map \DD \R$.

This would correspond to the following mapping:

$\ds \phi \stackrel {T_f} {\longrightarrow} \int_{-\infty}^\infty \map f x \map \phi x \rd x$

Sources

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• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 6.1$: A glimpse of distribution theory. Test functions, distributions, and examples