Abstract:
The monograph is devoted to investigation of asymptotic properties of positive functions represented by the Laplace-Stiltjes integrals. Important role of such integrals is well-known in mathematical and complex analysis, probability theory, number theory and in other regions of mathematics. Since the Laplace-Stieltjes integrals are direct generalization of the Laplace integral and the Dirichlet series with nonnegative coefficients and exponents, the investigation of the asymptotic properties of the Laplace-Stieltjes integrals is necessary and actual. The book is intended for graduate mathematical students, post-graduates and experts in the mathematical analysis and its applications. The necessary mathematical background for reading the monograph is a university course of calculus.

Contents:
Preface
1. Abscissa of convergence
2. Asymptotic behaviour of maximum of the integrand
3. Estimates of laplace-stiltjes integral by maximum of the integrand
4. Generalized order of growth
5. Logarithms of laplace-stiltjes integral and of maximum of the integrand
6. Rate of convergence
7. Asymptotical behaviour of remainders