On the finiteness of the discrete spectrum of a 3x3 operator matrix

Tulkin H. Rasulov

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arXiv · 1609.04277

On the finiteness of the discrete spectrum of a 3x3 operator matrix

Tulkin H. Rasulov

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Abstract

An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra of two families of the generalized Friedrichs models. A symmetric version of the Weinberg equation for eigenvectors of $H$ is obtained. The conditions which guarantee the finiteness of the number of discrete eigenvalues located below the bottom of the three-particle branch of the essential spectrum of $H$ is found.

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Tulkin H. Rasulov. 2016-09-14. On the finiteness of the discrete spectrum of a 3x3 operator matrix. https://arxiv.org/abs/1609.04277

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