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• W3021280644 abstract "We consider the family of $3 times 3$ operator matrices ${bf H}(K),$ $K in {Bbb T}^3:=(-pi; pi]^3$ associated with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. We find a finite set $Lambda subset {Bbb T}^3$ to prove the existence of infinitely many eigenvalues of ${bf H}(K)$ for all $K in Lambda$ when the associated Friedrichs model has a zero energy resonance. It is found that for every $K in Lambda,$ the number $N(K, z)$ of eigenvalues of ${bf H}(K)$ lying on the left of $z,$ $z<0,$ satisfies the asymptotic relation $limlimits_{z to -0} N(K, z) |log|z||^{-1}={mathcal U}_0$ with $0<{mathcal U}_0<infty,$ independently on the cardinality of $Lambda.$ Moreover, we prove that for any $K in Lambda$ the operator ${bf H}(K)$ has a finite number of negative eigenvalues if the associated Friedrichs model has a zero eigenvalue or a zero is the regular type point for positive definite Friedrichs model." @default.
• W3021280644 created "2020-05-13" @default.
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• W3021280644 date "2020-05-05" @default.
• W3021280644 modified "2023-09-27" @default.
• W3021280644 title "Analysis of the discrete spectrum of the family of $3 times 3$ operator matrices" @default.
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