A Note on Generalized Tauberian Theorems
C. T. Rajagopal · Proceedings of the American Mathematical Society · 1951
The condition A(0)=0 is included in the usual assumption that A(u) is normalized.2 The monotony of and the convergence of the integral in (ii) ensure that 4>(tt)->0 as îi->».Hence f¡${u)du exists, (u) -f2^(x)dx+ a constant, where the constant is seen to be 0 by making u-* °°.It may be noticed that the usual assumption, in addition to C(ii), of the existence of /o[l -4>(u)]/udu is implied in the fact lim"_o [l -(«)]/« = lim"-.o-4>'(u)= limUj.oi(u).