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Results tagged with schwartz-distributions
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user 140146
A distribution is a continuous linear functional on the space $\mathcal{C}^{\infty}_c$ of smooth (indefinitely differentiable) functions with compact support. Though they appeared in formal computations in the physics and engineering literature in the late $19^{th}$ century, their formal setting was brought up by the work of S. Sobolev and L. Schwartz in the middle of the $20^{th}$ century.
6
votes
2
answers
390
views
Fourier coefficients of a periodic distribution?
Let $\tau>0$, and let $T\in \mathcal{D}'(\mathbb{R})$ be a $\tau$-periodic distribution (that is,
$
\langle T, \varphi(\cdot+\tau)\rangle= \langle T,\varphi\rangle
$
for all $\varphi \in \mathcal{D …
- 115
2
votes
1
answer
206
views
Continuity of convolution on $\mathcal{D}'_+$
Let $\mathcal{D}'_+:=\{T\in \mathcal{D}'(\mathbb{R}): \textrm{supp}(T)\subset [0,\infty)\}$. Here $\mathcal{D}'(\mathbb{R})$ is the usual space of distributions on $\mathbb{R}$, equipped with the weak …
- 115