All Questions
4 questions
0
votes
0
answers
66
views
Lower bound of the derivative $(f*g_\sigma)'$ at the zero-crossing point
I am stuck with the following problem. Let consider $f$ a smooth real function such that:
$f$ is negative before 0,
$f$ is positive after 0,
we have $|f'(0)|>0$.
Let $\sigma>0$ and $g_\sigma$ ...
3
votes
0
answers
155
views
Inequality involving convolution roots
I am struggling with the following problem. Let $f$ be a real smooth function. Let assume that $f$ is:
increasing
strictly convex on $(-\infty,0)$
strictly concave on $(0,+\infty)$
Let $\sigma>0$ ...
2
votes
1
answer
112
views
Uniqueness of the zero of $f-f*G_\sigma$ with $f$ convex/concave
I am struggling with the following problem. Let $f$ be a real smooth function:
strictly convex on $(-\infty,0)$,
strictly concave on $(0,\infty)$,
strictly increasing.
For $\sigma>0$, how can one ...
3
votes
1
answer
220
views
Is there a real/functional analytic proof of Cramér–Lévy theorem?
In the book Gaussian Measures in Finite and Infinite Dimensions by Stroock, there is a theorem with a comment
The following remarkable theorem was discovered by Cramér and Lévy. So far as I know, ...