Operator interpretation of resonances generated by some operator matrices

Details Operator interpretation of resonances generated by some operator matrices Operator interpretation of resonances generated by some operator matrices

1998-09-17

arxiv.org/abs/math/9809093v1

Oper.Theor.Advan.Appl. 118 (2000) 287-302

Mathematics

Spectral Theory

LaTeX, 15 pages, no figures; Contribution to Proceedings of the Mark Krein International Conference on Operator Theory and App

Scientific paper

10.1007/BF02557129

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.

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