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, 1-14

Abstract:

A family ð » ð œ‡ ( ð ‘ ) , 𠜇 > 0 , ð ‘ âˆˆ ð •‹ 2 of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two-dimensional lattice ℤ 2 is considered. The existence or absence of the unique eigenvalue of the operator ð » ð œ‡ ( ð ‘ ) lying below threshold depending on the values of 𠜇 > 0 and ð ‘ âˆˆ 𠑈 ð ›¿ ( 0 ) ⊂ ð •‹ 2 is proved. The analyticity of corresponding eigenfunction is shown.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:180953

DOI: 10.1155/2012/180953

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