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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2021, 12 (2), P. 135–141

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

R. R. Kucharov – National University of Uzbekistan, 100174, Tashkent, Uzbekistan; ramz3364647@yahoo.com
R. R. Khamraeva – National University of Uzbekistan, 100174, Tashkent; Westminster International University in Tashkent, 100010, 12, Istiqbol str., Tashkent, Uzbekistan; r.khamraeva@wiut.uz

The change in the spectrum of the multipliers H0f(x; y) = xα +yβ f(x; y) and H0f(x; y) = xαyβ f(x; y) for perturbation with partial integral operators in the spaces L2[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.

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

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