Puiseux Series Expansion for Eigenvalue of the Generalized Friedrichs Model with the Perturbation of Rank One
Sh. Kh. KurbanovDepartment of Mathematics, Samarkand State University, 140104, Samarkand, UzbekistanSaid T. DustovDepartment of Mathematics and Computer Science, Navoi State Pedagogical Institute, 210102, Navoi, Uzbekistan
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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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