Convergent expansions of eigenvalues of the generalized Friedrichs model with a rank-one perturbation

Saidakhmat Lakaev; Shakhzod Kurbanov

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arXiv · 2004.08815

Convergent expansions of eigenvalues of the generalized Friedrichs model with a rank-one perturbation

Saidakhmat Lakaev·Shakhzod Kurbanov

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Abstract

We study the existence of eigenvalues of the generalized Friedrichs model $H_\mu(p)$, with a rank-one perturbation, depending on parameters $\mu>0$ and $p\in\mathbb{T}^2$, and found an absolutely convergent expansions for eigenvalues at $\mu(p)$, the coupling constant threshold. The expansions are highly dependent on that, whether the threshold $m(p)$ of the essential spectrum is: $(i)$ neither an threshold eigenvalue nor a threshold resonance; $(ii)$ a threshold resonance; $(iii)$ an threshold eigenvalue.

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BibTeX RIS

Saidakhmat Lakaev, Shakhzod Kurbanov. 2020-04-19. Convergent expansions of eigenvalues of the generalized Friedrichs model with a rank-one perturbation. https://arxiv.org/abs/2004.08815

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