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 Mat. Sb. (N.S.), 1985, Volume 126(168), Number 4, Pages 515–542 (Mi msb1949)

Multidimensional Tuberian comparison theorems for generalized functions in cones

Yu. N. Drozhzhinov, B. I. Zavialov

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1986, 54:2, 499–524

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: 40E05, 46F05, 46F12

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Tuberian comparison theorems for generalized functions in cones”, Mat. Sb. (N.S.), 126(168):4 (1985), 515–542; Math. USSR-Sb., 54:2 (1986), 499–524

Citation in format AMSBIB
\Bibitem{DroZav85} \by Yu.~N.~Drozhzhinov, B.~I.~Zavialov \paper Multidimensional Tuberian comparison theorems for generalized functions in cones \jour Mat. Sb. (N.S.) \yr 1985 \vol 126(168) \issue 4 \pages 515--542 \mathnet{http://mi.mathnet.ru/msb1949} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=788085} \zmath{https://zbmath.org/?q=an:0603.46045} \transl \jour Math. USSR-Sb. \yr 1986 \vol 54 \issue 2 \pages 499--524 \crossref{https://doi.org/10.1070/SM1986v054n02ABEH002982} 

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This publication is cited in the following articles:
1. A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371
2. Zavialov B., “On the Asymptotic Properties of Functions Holomorphic in Tubular Cones”, 294, no. 5, 1987, 1048–1050
3. B. I. Zavialov, “On the asymptotic properties of functions holomorphic in tubular cones”, Math. USSR-Sb., 64:1 (1989), 97–113
4. Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Abelian and Tauberian comparison theorems”, Math. USSR-Sb., 68:1 (1991), 85–110
5. A. L. Yakymiv, “Tauberian theorems and asymptotics of infinitely divisible distributions in a cone”, Theory Probab. Appl., 48:3 (2004), 493–505
6. A. L. Yakymiv, “Admissible Functions for the Positive Octant”, Math. Notes, 76:3 (2004), 432–437
7. Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. J., 7:3 (2015), 47–53
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