Geodesic
Towards the Tauberian theorem of Keldysh
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 63-89

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New versions of the Tauberian theorem of Keldysh are proved. We give examples to show the sharpness of the conditions of these theorems. Among auxiliary results, new cases of inversion of the de l'Hospital rule are obtained. 
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     author = {A. F. Grishin and I. V. Poedintseva},
     title = {Towards the {Tauberian} theorem of {Keldysh}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {63--89},
     publisher = {mathdoc},
     volume = {315},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a4/}
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A. F. Grishin; I. V. Poedintseva. Towards the Tauberian theorem of Keldysh. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 63-89. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a4/