# 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).

1answer
134 views

### Why the tempered distribution is zero?

My question is derived from the proof of the equation $\Delta f=f$ which has no nonzero solution in $\mathscr{S}'(\mathbb{R}^n)$. The ideal to solve this equation is to use the Fourier transform. By ...
1answer
42 views

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### Relationships between growth rates of a distribution and smoothness of its Fourier transform

Let $f\in \mathcal{S}^\prime(\mathbb{R})$ be a tempered distribution, and $\hat{f}$ be its Fourier transform. It is known that when both $f$ and $\hat{f}$ are $L^2$ functions, there are relationships ...
1answer
55 views

### About a condition for a distribution to be zero

I'm trying to solve the following question: If $S$ is a distribution with compact support on $\mathbb{R}$, which verifies $\langle S, x^n \rangle=0$ $\forall n\in\mathbb{N}$, then $S$ is the ...
2answers
211 views

1answer
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### Is $\delta : \mathcal{S}(\mathbf{R}) \to \mathbf{C}$ continuous with usual seminorm?

I am thinking again the accepted answer which is found here: When viewing $\delta: \mathbf{S} \to \mathbf{R}$ (linear and continuous with respect to the usual semi-norms on the Schwartz-space ...
2answers
38 views

### To write this sentence about a distribution more rigorously

I have the sentence at the moment Notice that for all $c \in \mathbf{C}$ such that $W(cx) = |c|^{2} Wx$. which I do not like. I mean to say that for all $c \in \mathbf C$ the equation is true. ...
1answer
88 views