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
kth 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
Ck+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(iθA) 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 (1971)
[3]. As a new application we consider the massive Spin-Boson Model.
