Geodesic
Non-compact perturbations of the spectrum of multipliers given with functions
Nanosistemy: fizika, himiâ, matematika, Tome 12 (2021) no. 2, pp. 135-141.

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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. 
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     author = {R. R. Kucharov and R. R. Khamraeva},
     title = {Non-compact perturbations of the spectrum of multipliers given with functions},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
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R. R. Kucharov; R. R. Khamraeva. Non-compact perturbations of the spectrum of multipliers given with functions. Nanosistemy: fizika, himiâ, matematika, Tome 12 (2021) no. 2, pp. 135-141. http://geodesic.mathdoc.fr/item/NANO_2021_12_2_a0/