Spectra of partial integral operators with a kernel of three variables

• Autorzy: Yusup Eshkabilov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

partial integral operator; partial integral equation; Fredholm integral equation; Fredholm determinant; Fredholm minor; spectrum; limit spectrum; point spectrum

Kategorie tematyczne

• 45P05: Integral operators
• 45B05: Fredholm integral equations
• 45A05: Linear integral equations
• 47A10: Spectrum, resolvent

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 1
• Strony: 149-157

Daty

wydano

2008-03-01

online

2008-02-26

Twórcy

autor

Yusup Eshkabilov

• National University of Uzbekistan

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-008-0010-3