Geodesic
The Simplest Tauberian Theorem
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 221-229

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The following problem is considered: obtain the asymptotic properties of a function $u$ from the asymptotic properties of the integral $\int_0^r{u(t)}dt$. As is well known, this can be done under additional constraints on the function $u(t)$. In this paper, we obtain a theorem in which these constraints are weaker than in other well-known versions of such theorems. 
@article{MZM_2003_74_2_a3,
     author = {A. F. Grishin},
     title = {The {Simplest} {Tauberian} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {221--229},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a3/}
}
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A. F. Grishin. The Simplest Tauberian Theorem. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 221-229. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a3/