Ukrainian Mathematical Bulletin
Volume 2, Issue 4, 2005 pp. 547-555.
Asymptotic Estimates for Laplace--Stieltjes IntegralsAuthors: Olena S. Posiko and Myroslav M. Sheremeta
Author institution: Olena S. Posiko, Myroslav M. Sheremeta, Lviv National University, 1 Universytets'ka Str., 79000, Lviv, Ukraine m_m_sheremeta@list.ru
Summary: Let a function $F$ be nonnegative, nondecreasing, unbound\-ed, and right-continuous on $[0,+\infty)$ and let a function $f$ be nonnegative on $[0,+\infty)$. We obtain asymptotic estimates for $ \ln \int_{0}^{\infty}f(x)e^{x\si}dF(x)$ in terms of $\ln \mu(\si)=\sup\{\ln f(x)+x\si:\ x\ge 0\}, \ \si\in{\Bbb R}$.
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