  The present paper gives an abstract method to prove that possibly embedded
eigenstates of a self-adjoint operator $H$ lie in the domain of the $k^{th}$
power of a conjugate operator $A$. Conjugate means here that $H$ and $A$ have a
positive commutator locally near the relevant eigenvalue in the sense of
Mourre. The only requirement is $C^{k+1}(A)$ regularity of $H$. Regarding
integer $k$, our result is optimal. Under a natural boundedness assumption of
the multiple commutators we prove that the eigenstate 'dilated' by
$\exp(i\theta A)$ is analytic in a strip around the real axis. In particular,
the eigenstate is an analytic vector with respect to $A$. Natural applications
are 'dilation analytic' systems satisfying a Mourre estimate, where our result
can be viewed as an abstract version of a theorem due to Balslev and Combes. As
a new application we consider the massive Spin-Boson Model.
