On the Eigenvalues of Integral Operators

Yıl 2006, Cilt: 1 Sayı: 6, 177 - 185, 01.06.2006

Yüksel Soykan

Öz

Anahtar Kelimeler

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On the Eigenvalues of Integral Operators

Öz

Bu çalışmada bazı positive integral operatörlerin özdeğerlerinin asimtotik yaklaşımlarını elde edeceğizFrom now on, let J be a fixed closed subinterval of the real line R. Suppose that D
is a simply-connected domain containing the real closed interval J and ϕ is any
function, which maps D conformally onto ∆, where ∆ is the open unit disk of complex
plane C. Let us define a function KD on D x D by
for either of the branches of The function KD is independent of the choice of mapping
function ϕ, see [1, p.410]. By restricting the function KD to the square JxJ we obtain a
compact symmetric operator TD on L2 defined by

Anahtar Kelimeler

Pozitif İntegral Operatörleri, Özdeğerler, Hardy Uzayları

Kaynakça

• Little, G., “Equivalences of positive integrals operators with rational kernels”, Proc. London. Math. Soc. (3) 62 (1991), 403-426.
• Duren, P. L., “Theory of spaces”, Academic Press, New York, 1970
• Koosis, P., “Introduction to spaces”, Cambridge University Press, Cambridge, Second Edition, 1998.
• Soykan Y., “An Inequality of Fejer-Riesz Type”, Çankaya University, Journal of Arts and Sciences, Issue: 5, May 2006, 51-60.