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Spectra of partial integral operators with a kernel of three variables

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Central European Journal of Mathematics

Abstract

Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in \( C \)(Ω): (T 1 f)(x, y) = \( \mathop \smallint \limits_a^b \) k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = \( \mathop \smallint \limits_c^d \) 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.

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  1. National University of Uzbekistan, Vuzgorodok, Tashkent, 100174, Uzbekistan

    Yusup Kh. Eshkabilov

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  1. Yusup Kh. Eshkabilov
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Eshkabilov, Y.K. Spectra of partial integral operators with a kernel of three variables. centr.eur.j.math. 6, 149–157 (2008). https://doi.org/10.2478/s11533-008-0010-3

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  • DOI: https://doi.org/10.2478/s11533-008-0010-3

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