# Definition:Tempered Distribution Space

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## Definition

Let $T: \map \SS \R \to \C$ be a tempered distribution.

Then the set of all $T$ is called the **tempered distribution space** and is denoted by $\map {\SS'} \R$.

Although this article appears correct, it's inelegant. There has to be a better way of doing it.In particular: But $T$ is fixed above. You can not talk about all $T$. Please correct the formality of the definition.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by redesigning it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Improve}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 2017: Amol Sasane:
*A Friendly Approach to Functional Analysis*... (previous) ... (next): Chapter $\S 6.5$: A glimpse of distribution theory. Fourier transform of (tempered) distributions