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Results tagged with convolution
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user 21907
10
votes
Accepted
Analyticity of $f*g$ with $f$ and $g$ smooth on $\mathbb{R}$ and analytic on $\mathbb{R}^*$
The answer to your question is negative. Take the smooth function $\chi$ defined by
$$
\chi(t)=H(t) e^{-t^{-1}-t^2}, \quad H=\mathbf 1_{(0,+\infty)}.
$$
This function is in $L^1(\mathbb R)$, $C^\infty …
- 16.2k
6
votes
3
answers
897
views
Convolution of $L^2$ functions
Let $u\in L^2(\mathbb R^n)$: then $u\ast u$ is a bounded continuous function. Let me assume now that $u\ast u$ is compactly supported. Is there anything relevant that could be said on the support of $ …
- 16.2k
2
votes
0
answers
66
views
Classifying Algebras of Convolution
$L^1(\mathbb R^n)$, $L^1(\mathbb R_+)$, $C^0_c(\mathbb R_+)$, $C^\infty_c(\mathbb R_+)$ are algebras of convolution. … Question 1: is there a classification of subalgebras of convolution of $L^1(\mathbb R^n)$? …
- 16.2k