Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One

Saidakhmat Lakaev, Arsmah Ibrahim and Shaxzod Kurbanov

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: A family Hμ(p), μ > 0, p ∈ 𝕋2 of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two‐dimensional lattice ℤ2 is considered. The existence or absence of the unique eigenvalue of the operator Hμ(p) lying below threshold depending on the values of μ > 0 and p ∈ Uδ(0) ⊂ 𝕋2 is proved. The analyticity of corresponding eigenfunction is shown.

Date: 2012
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https://doi.org/10.1155/2012/180953

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:180953

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