Two-member asymptotic of Laplace-Stieltjes integrals

Author
M. M. Sheremeta, M. S. Dobushovskyy
Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract
We study conditions, under which for the Laplace-Stieltjes integral $I(\sigma)=\int_{0}^{\infty}\!f(x)e^{x\sigma}dF(x)$ with the abscissa of the convergence $\sigma_c=A\in (-\infty,+\infty]$ the asymptotical equality $\ln\,I(\sigma)=\Phi_1(\sigma)+\tau(1+o(1))\Phi_2(\sigma)$ as $\sigma\uparrow A$ is true, where $\tau\in{\Bbb R}\setminus\{0\}$ and $\Phi_1,\,\Phi_2$ are some positive functions on $(-\infty,A)$.
Keywords
Laplace-Stieltjes integral; two-member asymptotic
DOI
doi:10.15330/ms.47.1.3-9
Reference
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6. Dobushovskyy M.S., Sheremeta M.M. Estimates of Laplace-Stieltjes integrals// Ukr. Mat. J. - 2016. - V.68, 11. - P. 1467-1482, (in Ukrainian); Engl. Transl.: Ukr. Math. Zh. - 2017. - V.68, 11. - P. 1694-1714.

7. Sheremeta M.M., Dobushovskyy M.S. On the two-member asymptotics of Young conjugated functions// Mat. Stud. - 2016. - V.46, 2. - P. 178-188.

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Pages
3-9
Volume
47
Issue
1
Year
2017
Journal
Matematychni Studii
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