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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Is this operator a distribution?

Is this operator: $$T: \mathcal{C}^{\infty}_0 \ni \varphi \to \lim_{x \to \infty} x^2 e^{-x} \varphi'(x) \in \mathbb{R}$$ a distribution (generalized function)? I need to check two things: whether ...
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Limit of $\frac{1}{x+i y}$ for $y \rightarrow 0$ and distributional relations

So I know for $y \rightarrow 0$ I have the following (distrubutional) relation: $\frac{1}{x+i y} = \frac{x}{x^2+y^2} - i \frac{y}{x^2+y^2} = P(1/x) - i \pi \delta(x)$ where in the last expression ...
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cutoff function vs mollifiers

Q1. What are cutoff function? What are mollifiers? I cannot distinguish the two. Could anyone give some concrete/simple examples of cutoff functions? And how they differ from mollifiers I did check ...
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What is the Fourier transform of $\exp(2 \pi i / x)$?
The Fourier transform of $e^{2 \pi i / x}$ makes sense as a distribution, I believe. Does it have a nice expression in terms of functions and well-known distributions (e.g. Dirac delta)?
Here is a small result annoying me : Let $u$ be a distribution ($u \in \mathcal{D}'(\mathbb{R}^n)$) such that $\Delta u$ is continuous. Then $u$ is continuous. I am not able to prove this, and ...