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

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Abstract

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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Funding

The authors acknowledge support from the Foundation for Basic Research of the Republic of Uzbekistan (Grant no. FZ-20200929224).

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Authors and Affiliations

  1. Department of Mathematics, Samarkand State University, 140104, Samarkand, Uzbekistan

    Sh. Kh. Kurbanov

  2. Department of Mathematics and Computer Science, Navoi State Pedagogical Institute, 210102, Navoi, Uzbekistan

    S. T. Dustov

Authors
  1. Sh. Kh. Kurbanov
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  2. S. T. Dustov
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Corresponding authors

Correspondence to Sh. Kh. Kurbanov or S. T. Dustov.

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(Submitted by T. K. Yuldashev)

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Kurbanov, S.K., Dustov, S.T. Puiseux Series Expansion for Eigenvalue of the Generalized Friedrichs Model with the Perturbation of Rank One. Lobachevskii J Math 44, 1365–1372 (2023). https://doi.org/10.1134/S1995080223040157

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