The threshold effects for a family of Friedrichs models under rank one perturbations |
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| Authors: | Sergio Albeverio Saidakhmat N. Lakaev Zahriddin I. Muminov |
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| Affiliation: | aInstitut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany;bSFB 611, Universität Bonn, BiBoS, Bielefeld, Bonn, Germany;cCERFIM, Locarno and Acc.ARch,USI, Switzerland;dSamarkand State University, University Boulevard 15, 703004 Samarkand, Uzbekistan;eSamarkand Division of Academy of Sciences of Uzbekistan, Uzbekistan |
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| Abstract: | A family of Friedrichs models under rank one perturbations hμ(p), p (−π,π]3, μ>0, associated to a system of two particles on the three-dimensional lattice  is considered. We prove the existence of a unique eigenvalue below the bottom of the essential spectrum of hμ(p) for all non-trivial values of p under the assumption that hμ(0) has either a threshold energy resonance (virtual level) or a threshold eigenvalue. The threshold energy expansion for the Fredholm determinant associated to a family of Friedrichs models is also obtained. |
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| Keywords: | Family of Friedrichs models Eigenvalues Energy resonance Pair non-local potentials Conditionally negative definite functions |
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