On the Eigenvalues of Integral Operators

Özet

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 Dis a simply-connected domain containing the real closed interval J and ϕ is anyfunction, which maps D conformally onto ∆, where ∆ is the open unit disk of complexplane C. Let us define a function KD on D x D byfor either of the branches of The function KD is independent of the choice of mappingfunction ϕ, see [1, p.410]. By restricting the function KD to the square JxJ we obtain acompact symmetric operator TD on L2 defined by