Dilation analytic interactions

E. Balslev, J. Combes, Spectral properties of many-body Schrodinger operators with dilation-analytic interactions, Commun. Math. Phys. 22 (1971) 280. 

In order to appreciate the fine points in this analysis, we therefore return to the domain issues, i.e. how to define the operator and the basis functions so that the scaling operation above becomes meaningful. Following Balslev and Combes [3], we introduce the N-body (molecular) Hamiltonian as H = T + V, where T is the kinetic energy operator and V is the (dilatation analytic) interaction potential (expressed as sum of two-body potentials Vy bounded relative Ty = Ay, where the indices i and j refers to particles i and j respectively). As a first crucial point we realize that the complex scaling transformation is unbounded, which necessitates a restriction of the domain of H note that H is normally bounded from below. Hence we need to specify the domain of H as... 

E. BalsIevandJ.M. Combes, Commun. Math. Phys., 22,280-294(1971). Spectral Properties of Many-Body Schrodinger Operators with Dilatation-Analytic Interactions. 

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