Geodesic
Multidimensional Tuberian comparison theorems for generalized functions in cones
Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 499-524 
Yu. N. Drozhzhinov; B. I. Zavialov. Multidimensional Tuberian comparison theorems for generalized functions in cones. Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 499-524. http://geodesic.mathdoc.fr/item/SM_1986_54_2_a11/
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     title = {Multidimensional {Tuberian} comparison theorems for generalized functions in cones},
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     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_2_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article deals with the proofs of some multidimensional Tauberian comparison theorems for generalized functions with supports in homogeneous cones, in particular, for measures and functions whose Laplace transforms have nonnegative imaginary parts. “Admissible” generalized functions, which can be regarded as multidimensional analogues of the so-called $R$-$O$-functions of Karamata, serve as comparison functions in these theorems. For circular and $n$-faced cones a criterion is obtained for admissibility which generalizes the well-known Keldysh Tauberian condition to the multidimensional case. Bibliography: 9 titles.

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[2] Drozhzhinov Yu. N., Zavyalov B. I., “Tauberovy teoremy dlya obobschennykh funktsii s nositelyami v konusakh”, Matem. sb., 108(150) (1979), 78–90 | MR | Zbl

[3] Drozhzhinov Yu. N., “Mnogomernaya tauberova teorema dlya golomorfnykh funktsii ogranichennogo argumenta i kvaziasimptotika passivnykh sistem”, Matem. sb., 117(259) (1982), 55–59 | MR

[4] Kozlov S. M., “Mnogomernye spektralnye asimptotiki dlya ellipticheskikh operatorov”, DAN SSSR, 268:4 (1983), 789–793 | MR | Zbl

[5] Yakymiv A. L., “Mnogomernye tauberovy teoremy tipa Karamata, Keldysha i Littlvuda”, DAN SSSR, 270:3 (1983), 358–361 | MR

[6] Keldysh M. V., “Ob odnoi tauberovoi teoreme”, Tr. MIAN, 38 (1951), 77–86 | Zbl

[7] Kostyuchenko A. G., Sargsyan I. S., Raspredelenie sobstvennykh znachenii, Nauka, M., 1979 | MR | Zbl

[8] Subkhankulov M. A., Tauberovy teoremy s ostatkom, Nauka, M., 1976 | MR

[9] Seneta E., Regulary Varying Functions, Lecture Notes in Math., Springer-Verlag, Berlin, 1976, p. 508 | MR