Estimation of the Laplace-Stieltjes integrals. (English. Ukrainian original) Zbl 1490.26007
Ukr. Math. J. 68, No. 11, 1694-1714 (2017); translation from Ukr. Mat. Zh. 68, No. 11, 1467-1482 (2016).
Summary: We study the Laplace-Stieltjes integrals with an arbitrary abscissa of convergence. The lower and upper estimates for these integrals are established. The accumulated results are used to deduce the relationships between the growth of the integral and the maximum of the integrand.
MSC:
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
References:
| [1] | M. M. Sheremeta, Asymptotical Behavior of Laplace-Stieltjes Integrals, VNTL Publ., Lviv (2010). · Zbl 1316.44001 |
| [2] | O. B. Skaskiv and A. I. Bandura, Asymptotic Estimates for Positive Integrals and Entire Functions [in Ukrainian], Lviv-Ivano-Frankivs’k, LNY-IFNTUG (2015). · Zbl 1327.32004 |
| [3] | O. B. Skaskiv and A. I. Bandura, Asymptotical Behavior of Laplace-Stieltjes Integrals, VNTL Publ., Lviv (2010). · Zbl 1316.44001 |
| [4] | M. N. Sheremeta and S. I. Fedynyak, “On the derivative of the Dirichlet series,” Sib. Mat. Zh., 39, No. 1, 206-223 (1998). · Zbl 0940.30014 · doi:10.1007/BF02732373 |
| [5] | M. M. Sheremeta and O. M. Sumyk, “Relationship between functions conjugate in Young’s sense,” Mat. Stud., 11, No. 1, 41-47 (1999). · Zbl 0974.30516 |
| [6] | M. M. Sheremeta, Yu. V. Stets, and O. M. Sumyk, “Estimates of a sum of Dirichlet series,” Ukr. Math. Bull., 10, No. 2, 234-253 (2013). · Zbl 1304.30006 |
| [7] | Yu. V. Stets’ and M. M. Sheremeta, “On the regular growth of Dirichlet series absolutely convergent in a half plane,” Ukr. Mat. Zh., 63, No. 5, 686-698 (2011); English translation: Ukr. Math. J., 63, No. 5, 797-814 (2011). · Zbl 1243.30005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
