I have a problem proving that some specific kernels are positive definite. In general, I can find the answer quickly enough but here I have a specific case involving a logartihm :
$K:\mathbb{R}_+\times\mathbb{R}_+$ with $K(x,y)=\log(1+xy)$ I've tried a lot of different things (using series, writing it as an integral), but it seems to be impossible to prove it.
Thanks for helping me