Geodesic
Tauberian theorems for generalized functions with supports in cones
Sbornik. Mathematics, Tome 36 (1980) no. 1, pp. 75-86 
Yu. N. Drozhzhinov; B. I. Zavialov. Tauberian theorems for generalized functions with supports in cones. Sbornik. Mathematics, Tome 36 (1980) no. 1, pp. 75-86. http://geodesic.mathdoc.fr/item/SM_1980_36_1_a4/
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     title = {Tauberian theorems for generalized functions with supports in~cones},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article the authors prove several multidimensional theorems of Tauberian type, connecting the behavior at infinity of generalized functions with support in a cone with the behavior of their Fourier–Laplace transforms in a neighborhood of zero. As corollaries they deduce a strengthened version of V. S. Vladimirov's Tauberian theorem and an analog of the theorem of Lindelöf for the edge of a tube domain over a cone. Bibliography: 5 titles.

[1] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, izd-vo “Nauka”, Moskva, 1976 | MR

[2] Yu. N. Drozhzhinov, B. I. Zavyalov, “Kvaziasimptotika obobschennykh funktsii i tauberovy teoremy v kompleksnoi oblasti”, Matem. sb., 102(144) (1977), 372–390 | Zbl

[3] V. S. Vladimirov, “Mnogomernoe obobschenie tauberovoi teoremy Khardi i Littlvuda”, Izv. AN SSSR, seriya matem., 40 (1976), 1084–1101 | MR | Zbl

[4] E. M. Chirka, “Teoremy Lindelefa i Fatu v $\mathbf C^n$”, Matem. sb., 92 (134) (1973), 622–644 | Zbl

[5] S. Lojasiewicz, “Sur la valeur et limite d'une distribution dans une point”, Studia Math., 16:1 (1957), 1–36 | MR | Zbl