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Results tagged with schwartz-distributions
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user 317800
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.
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Fourier transform of periodic distributions
This is a comment rather than an answer but it will be too long. There is a confusion in your statement which I find rather irritating and which has not, as far as I can see, been addressed here. I …
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What do we know about the space of finite order distributions ?
The following are some night thoughts on finite order distributions which might be of interest since this topic is a rich source of fruitful questions on the relations between abstract functional anal …
- 406
1
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Delta-distribution composed with a function from the Fourier representation
The point of this coda to the above answers is to document the fact that it is possible to address this topic in a perfectly rigorous and elementary fashion. Let me start with the remarks that there …
- 406
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Given a compact set $K \subset \mathbb{R}^n$, is the space of distributions supported on $K$...
The short answer to your question is yes. There is such a space, that of the locally smooth functions on $K$.
Let us recall that Schwartz defined the space of distributions with support in $K$ not di …
- 406
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Distributions as derivatives
This is perhaps tangential to your query but I am posting it in the hope that it might contain useful information. I will start with the case of distributions on a compact interval, which we can assu …
- 406