Puiseux Series Expansion for Eigenvalue of the Generalized Friedrichs Model with the Perturbation of Rank One

A family $$H_{\mu}(p)$$ , $$\mu>0$$ , $$p\in\mathbb{T}^{3}$$ of the Generalized Friedrichs models with the perturbation of rank one is considered. An absolutely convergent expansion for eigenvalue at the coupling constant threshold $$\mu(p)$$ is obtained. The expansion largely depends on whether the lower bound of the essential spectrum is a threshold resonance or a threshold eigenvalue.

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