Factorization theorem for the transfer function of a 2x2 operator matrix with unbounded couplings

Abstract

We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which factorize the transfer function and reproduce certain parts of its spectrum including the nonreal (resonance) spectrum situated in the unphysical sheets neighboring the physical sheet.

LaTeX2e, 14 pages, no figures