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Z ef(y)dy G(x) Finally, dividing by ey gives u(x;y) = e y Z eyf(y)dy e yG(x) = F(y) e yG(x);X 4 k(x,z) = g(x)g(z), for g X !Ie, f Rn!Ris convex if g( ) = f(x 0 v) is convex 8x 0 2dom(f) and 8v2Rn We just proved this happens i g00( 2) = vTrf(x 0 v)v 0; Function Composition Wikipedia G x z x 0 f t dt
