Abstract
A lemma is formulated on the asymptotic behavior of functions of class “R”; this lemma is then used for strengthening a well-known Tauberian theorem of Keldysh type for a two-sided Stieltjes transform.
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Literature cited
T. Selander, “Bilateral Tauberian theorems of Keldys type,” Arkiv Math.,5, 85–96 (1963).
I. S. Kats, “On integral representations of analytic functions that map the upper half-plane into part of it,” Uspekhi Matem. Nauk,11, No. 3, 139–144 (1956).
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M. V. Keldysh, “On a Tauberian theorem,” Tr. Matem. Inst. Akad. Nauk SSSR,38, 77–86 (1951).
Additional information
Translated from Matematicheskie Zametki, Vol. 15, no. 2, pp. 187–190, February, 1974.
The author expresses his gratitude to Professor A. G. Kostyuchenko.
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Belogrud', V.P. A tauberian theorem. Mathematical Notes of the Academy of Sciences of the USSR 15, 105–107 (1974). https://doi.org/10.1007/BF02102387
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DOI: https://doi.org/10.1007/BF02102387