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Results tagged with generalized-functions
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user 36721
2
votes
Accepted
Description of $\mathcal{S}^{2}_0(\mathbb{R})$ and certain class of functions inside it
$\newcommand\S{\mathcal S}\newcommand\R{\mathbb R}$For $x\in(0,1)$, let $g(x):=\frac1x$, and then let
$$f(x):=e^{-g(x)-g(1-x)}$$
for $x\in(0,1)$, with $f(x):=0$ for real $x\notin(0,1)$.
Then $f\in\S_0 …
- 128k
2
votes
What is the distribution of the following limit?
$\newcommand{\ep}{\epsilon}\newcommand{\de}{\delta}\newcommand{\R}{\mathbb{R}}$Let
\begin{equation*}
K_\ep(x):=\frac{\ln^m(x-i\ep)}{x-i\ep}-\frac{\ln^m(x+i\ep)}{x+i\ep}.
\end{equation*}
Let us sh …
- 128k