Operator interpretation of resonances generated by some operator matrices
arXiv:math/9809093 · doi:10.1007/BF02557129
Abstract
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.
LaTeX, 15 pages, no figures; Contribution to Proceedings of the Mark Krein International Conference on Operator Theory and Applications, Odessa, August 18-22, 1997
References in corpus (3)
- Removal of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian
- Representations for the Three-Body T-Matrix, Scattering Matrices and Resolvent in Unphysical Energy Sheets
- Operator interpretation of resonances arising in spectral problems for 2 x 2 operator matrices