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8-function Appl applies to equation approach zero Arthur Erdelyi assumption belong bounded Cauchy principal values Consequently consider constant continuous derivatives cp(x defined denote distributions Doctor of Philosophy eigenlimits entire function equa equivalent everywhere example existence of solutions exponential type f(x+l fact factored finite interval Fourier transform Fredholm equation Fredholm type function k(|x given gives Graduate Division half plane Hankel function heuristic inequality integral equations interval a,b inverse transform K(co kernel L-class less log a-jt log K(u lower half-plane main theorems Marvin Shinbrot Math method n(a+t n(x+t non-zero notation Ordinary differential equations ordinary function positive problem of diffraction proof of theorem properties real axis restriction ri(t ri(x satisfies second kind shown solu solution to exist Stanford theorem 5.1 tion trans unique solution upper half valid values whole real Wiener-Hopf equation zero at infinity