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Results tagged with schwartz-distributions
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user 18943
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
Accepted
Is the space of test functions separable?
I suppose, you mean the usual topology on $D({\mathbb R}^n)$ defined for example in Rudin's book. Take $D_N=\{\varphi\in D({\mathbb R}^n):\ {\rm supp}\varphi\subseteq\{x\in{\mathbb R}^n:\ |x|\le N\} \ …
- 7,426
1
vote
Topology on the space of Schwartz Distributions
Concerning this: "I am likewise interseted in the operator algebra of operators on S* that restrict to operators on S. In particular, I would like to abstractly characterize this space"
I am not sure …
- 7,426
3
votes
Completion of $\mathcal{S}(\mathbb{R})$ for a given norm
I am not sure that this is what you want, but it's too long for a comment, so I post it as an answer.
I don't see serious problems. If the conditions in terms of the theory of topological vector spa …
- 7,426
4
votes
Trace on $\mathcal{S}(\mathbb{R}^k) \mathbin{\hat{\otimes}_\pi} \mathcal{S}'(\mathbb{R}^k)$
In the "classical theory of topological vector spaces" the questions like this are intricated (in my opinion, this is an artifical complexity, the Nature can't be so complicated). But in the theory of …
- 7,426
13
votes
Understanding Bruhat's notion of Schwartz function
I strongly recommend you to read the François Bruhat paper, that Osborne cites. For an arbitrary locally compact (not necessarily abelian) group $G$ Bruhat defines smooth function $\varphi:G\to{\mathb …
- 7,426