MATHEMATICS

Non-compact perturbations of the spectrum of multipliers given with functions

R. R. Kucharov^a, R. R. Khamraeva<sup>ab

a</sup> National University of Uzbekistan, 100174, Tashkent, Uzbekistan
^b Westminster International University in Tashkent, 100010, 12, Istiqbol str., Tashkent, Uzbekistan

Abstract: The change in the spectrum of the multipliers $H_0f(x,y)=x^\alpha+y^\beta f(x,y)$ and $H_0 f(x,y)=x^\alpha y^\beta f(x,y)$ for perturbation with partial integral operators in the spaces $L_2[0,1]^2$ is studied. Precise description of the essential spectrum and the existence of simple eigenvalue is received. We prove that the number of eigenvalues located below the lower edge of the essential spectrum in the model is finite.

Keywords: essential spectrum, discrete spectrum, lower bound of the essential spectrum, partial integral operator.

Received: 25.01.2021
Revised: 10.03.2021
Accepted: 12.03.2021

Language: English

DOI: 10.17586/2220-8054-2021-12-2-135-141

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