About the spectral properties of one three-partial model operator

G. P. Arzikulov^a, Yu. Kh. Eshkabilov<sup>b

a</sup> Tashkent State Technical University named after Islam Karimov, 2 Universitetskaya str., Tashkent, 100097 Republic of Uzbekistan
^b Karshi State University, 17 Kuchabog str., Karshi, 180100 Republic of Uzbekistan

Abstract: We investigate the structure of the essential spectrum of one of the three particle model operator $H$. We prove the existence of a negative eigenvalues of the operator H and obtaine the estimate for a number of negative eigenvalues of the operator $H$.

Keywords: essential spectrum, discrete spectrum, lower bound of the essential spectrum, three particle discrete operator.

UDC: 517.984

Received: 18.05.2019
Revised: 29.10.2019
Accepted: 18.12.2019

DOI: 10.26907/0021-3446-2020-5-3-10

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:5, 1–7

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