# Tagged Questions

Use this tag for questions about distributions (or generalized functions). For questions about "probability distributions", use (probability-distributions). For questions about distributions as sub-bundles of a vector bundle, use (differential-geometry).

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### Why is $f(x) \delta(x) = f(0)\delta(x)$ only true when $x=0$?

This is a follow up from a previous question asked by me. I know that $$\delta(x) = \begin{cases} 0 & \space \mathrm{for} \space x \ne 0 \\\infty&\ \mathrm{for} \space x = 0 \end{cases}$$ ...
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### Rudin's application of the mean value theorem

I am studying theorem 6.26 (page 152) in Rudin's "Functional Analysis" that presents distributions as derivatives of continuous functions. Right at the beginning of the proof, if $\Omega$ is the ...
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### Is the map $\mathbb R^n\longrightarrow \mathscr{D}^\prime(\mathbb R^n)$, $x\longmapsto k(x, \cdot)$, continuous?

Recall, $a\in C^\infty(\mathbb R^n\times \mathbb R^n)$ is a symbol of order $m\in\mathbb R$ if for every $\alpha, \beta\in\mathbb N_0^n$ there is $C_{\alpha, \beta}>0$ such that ...
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### Computing the Fourier transform of the distribution $\|x\|^{-\alpha}$.

Question: Suppose we are given the tempered distribution $\|x\|^{-\alpha}$. We want to compute the Fourier transform $\mathcal{F}[\|x\|^{-\alpha}](\xi)$. What techniques are available for ...
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### normal form of currents

(question now crossposted to mathoverflow ) Let $M$ be an $n$-dimensional manifold. Then the space of currents $\mathcal D^k(M)$ of degree $k$ on $M$ is the space of continuous linear functionals on ...
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### Is $F(x)= \frac{1}{|x|^{r}}, (x\in \mathbb R)$ a distributiuon?

Does it make sense to talk of $F(x)= \frac{1}{|x|^{r}}, (x\in \mathbb R)$ for some $r>0$ in the sense of distribution? (I am just confused about the origin) (I mean, Is $F$ a distribution? If yes, ...