Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in (Ω): (T 1 f)(x, y) = k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded operators T 1, T 2, and T = T 1 + T 2 are proved.
@article{bwmeta1.element.doi-10_2478_s11533-008-0010-3,
author = {Yusup Eshkabilov},
title = {Spectra of partial integral operators with a kernel of three variables},
journal = {Open Mathematics},
volume = {6},
year = {2008},
pages = {149-157},
zbl = {1142.45001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0010-3}
}
Yusup Eshkabilov. Spectra of partial integral operators with a kernel of three variables. Open Mathematics, Tome 6 (2008) pp. 149-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0010-3/
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