Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences


We consider a family of discrete Schrödinger operators $H(K),\,K\in (-\pi,\pi]^5$ associated with a system of three quantum particles on the five-dimensional lattice ${\mathbb{Z}}^5$ interacting via short-range pair potentials and having arbitrary "dispersion functions" with not necessarily compact support.

We show that the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),\,K\in (-\pi,\pi]^5$ consists of a finitely many bounded closed intervals.

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