Threshold effects for the generalized friedrichs model with the perturbation of rank one
A family H μ (p), μ > 0, p ∈ 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 H,μ (p) lying below threshold depending on...
| Published in: | Abstract and Applied Analysis |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
2012
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| Online Access: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84866979615&doi=10.1155%2f2012%2f180953&partnerID=40&md5=d55ac225c7c66a6a230b59257f545b53 |
| Summary: | A family H μ (p), μ > 0, p ∈ 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 H,μ (p) lying below threshold depending on the values of μ > 0 and p ∈ U δ (0) ⊂ 2 is proved. The analyticity of corresponding eigenfunction is shown. © 2012 Saidakhmat Lakaev et al. |
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| ISSN: | 16870409 |
| DOI: | 10.1155/2012/180953 |