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Results tagged with schwartz-distributions
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user 150264
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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Integral representation of tempered distributions
After my previous post I got curious about the following very simple question (which I don't seem to find the answer). Given a tempered distribution $K \in \mathcal{S}'(\mathbb{R}^{n_{1}+\cdots+n_{N}} …
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Representation of a Schwartz map in terms of a kernel
Suppose $f: \mathcal{S}(\mathbb{R}^{d})^{n+1} \to \mathbb{C}$ is a continuous function. To each $\varphi \in \mathcal{S}(\mathbb{R}^{d})$, we can define the map $f[\varphi]: \mathcal{S}(\mathbb{R}^{d} …
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Mathematical meaning for the (continuous) Sine-Gordon transformation
I've been trying to understand the so-called Sine-Gordon Transformation which occurs in both classical and quantum statistical mechanics. One of the most cited references on this topic seems to be Frö …
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