The finiteness of the discrete spectrum of a model operator associated with a system of three particles on a lattice. (English. Russian original) Zbl 1298.47009
Russ. Math. 58, No. 1, 52-59 (2014); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2014, No. 1, 61-70 (2014).
Summary: We consider a model operator \(H\) associated with a system of three particles on a lattice interacting via nonlocal pair potentials. Under some natural conditions on the parameters specifying this model operator \(H\), we prove the finiteness of its discrete spectrum.
MSC:
| 47A10 | Spectrum, resolvent |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
Keywords:
discrete spectrum; nonlocal potential; continuity in the uniform operator topology; Hilbert-Schmidt class; Weinberg equationReferences:
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