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Results tagged with schwartz-distributions
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user 61785
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.
3
votes
Accepted
Convergence in $\sigma(\mathcal{E}',\mathcal{E})$ versus $\beta(\mathcal{E}',\mathcal{E})$
The answer is yes. First, since $\newcommand{E}{\mathcal{E}}\E$ is a Fréchet space, it is barrelled, and so any $\sigma(\E',\E)$-bounded subset of $\E'$ is equicontinuous, and therefore bounded in any …
- 3,768
1
vote
Topology of ${\mathcal D}(\Omega)$ (space of test functions)
There's a general principle for proving that a topology on a vector space $E$ is not a weak topology (in the general sense, a topology of the form $\sigma(E,F)$ for some $F \subseteq E^*$).
For $\sigm …
- 3,768