Аннотация:
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.
Ключевые слова:essential spectrum, discrete spectrum, lower bound of the essential spectrum, partial integral operator.
Поступила в редакцию: 25.01.2021 Исправленный вариант: 10.03.2021 Принята в печать: 12.03.2021