# Operator Interpretation of Resonances Arising in Spectral Problems for 2 x 2 Matrix Hamiltonians

@article{Motovilov1998OperatorIO, title={Operator Interpretation of Resonances Arising in Spectral Problems for 2 x 2 Matrix Hamiltonians}, author={Alexander K. Motovilov and Reinhard Mennicken}, journal={Operator theory}, year={1998}, volume={108}, pages={315-322} }

We consider the analytic continuation of the transfer function for a 2 x 2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer function which reproduce certain parts of its spectrum including resonances situated in 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…

## 3 Citations

### On invariant graph subspaces of a J-self-adjoint operator in the Feshbach case

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We consider a J-self-adjoint 2 × 2 block operator matrix L in the Feshbach spectral case, that is, in the case where the spectrum of one main-diagonal entry of L is embedded into the absolutely…

### On the Riccati equations

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- 2008

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