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Results tagged with schwartz-distributions
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user 49628
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
When sequentially continuous linear functional is continuous?
It is continuous even for the strong topology. This follows from general locally convex space theory, in particular from the fact that the space of smooth functions is a nuclear Fréchet space. Its d …
- 454
4
votes
Accepted
Linear operators on distributions with different topologies
The answer to all of your questions is no. This follows from the simple fact that if a linear mapping from a locally convex space $E$ into a normed space $F$ is continuous for the weak topology on $E …
- 454