Dobushovskyy M. Asymptotical properties of the Laplace-Stieltjes integral.

In this PhD thesis Laplace-Stieltjes integrals with an arbitrary abscissa of the convergence, new the lower and upper estimates are obtained. The accumulated results are used to deduce the relationships between the growth of the integral and the maximum of the integrand. In the terms of two-member asymptotic it is shown a connection between the behavior of Young conjugated functions and used the results for studying two-member asymptotic of Laplace- Stieltjes integral. For the Laplace-Stieltjes integrals analogues of the Whittaker theorem of order and the lower order of an entire function presented by lacunar series are obtained . We obtain formulas to nd the abscissa of the convergence of the Laplace-Stieltjes integral.