On the Eigenvalues of Integral Operators

Year 2006, Volume: 1 Issue: 6, 177 - 185, 01.06.2006

Yüksel Soykan

Abstract

Keywords

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On the Eigenvalues of Integral Operators

Abstract

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

Keywords

Pozitif İntegral Operatörleri, Özdeğerler, Hardy Uzayları

References

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• 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.