2010/06/02 by Jacob Moeller, Jacob S. Moeller, Moeller, Jacob S. +2
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1006.0410
27 pages
openalex publication_date 2010/06/02 · arxiv created 2010/07/02 · arxiv updated 2010/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. As a new application we consider the massive Spin-Boson Model.