Resolutions of identity for some non-Hermitian Hamiltonians II: proofs

A.V. Sokolov

This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration were taken with continuous spectrum and the following cases were examined: an exceptional point situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.

http://arxiv.org/abs/1107.5916
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Nuclear Theory (nucl-th); Quantum Physics (quant-ph)

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