is this formula correct ??
$$ \int_{-\infty}^{\infty} Lf(x)\delta (x-1)= \int_{-\infty}^{\infty} f(x)L^{\dagger}\delta(x-1) $$
here $ L $ is a linear operator and $ L^{\dagger}$ is its formal adjoint
for excample can someone provide some help whenever $ L = \Theta ^{n} $ and $ \Theta = x \frac{d}{dx} $ to find its self adjoint ??
also for example if i set $ f(x)= Li_{-s}(x) $ polyologarithm i guess the integral in the end should be equal to $ \zeta (s) $