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Results tagged with convolution
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user 127334
1
vote
Accepted
Limit of an integral / Boundary behaviour of a Gaussian convolution / single layer potential
First note that
$$ \partial_x k(s, x) = -\frac{x}{s}k(s,x),
\quad s > 0, x \in {\mathbb R},$$
so your integral becomes
$$
q_a(t,x) := \int^t_0 \partial_x k(s,x-a)k(t-s,a)ds.
$$
Now suddenly your …
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