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- W1985487509 abstract "Consider a Fredholm, integral equation for f(t, b) with a composite displacement kernel f(t,b)=g(t)+λ∫ab[E(t,y)+F(t+y)] f(y,b)dy, where g(t) is a given forcing function, the parameter λ is defined over 0<λ≤1,0≤a≤t≤b, and the E and F functions are together the displacement kernels. Extending the invariant imbedding method given in our preceding paper [cf. Bellman, Kagiwada, Kalaba, and Ueno, J. Math Phys. 9, 906 (1968)], we show how the Bellman-Krein formula provides us with a Cauchy system of the functional equations governing the resolvent and the scattering function. The invariant imbedding equations for the scattering function and the auxiliary function for a = 0 reduce to those given in a preceding paper [cf. Casti, Kalaba, and Ueno J. Quant. Spectry. Radiative Transfer 9, 537 (1969)], which treated with the diffuse reflection and transmission of radiation by a finite isotropically scattering atmosphere bounded by a specular reflector at the bottom." @default.
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- W1985487509 date "1973-11-01" @default.
- W1985487509 modified "2023-09-25" @default.
- W1985487509 title "Invariant imbedding and the resolvent of Fredholm integral equation with composite symmetric kernel" @default.
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- W1985487509 doi "https://doi.org/10.1063/1.1666212" @default.
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