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

This article is cited in 7 scientific papers (total in 7 papers)

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
Received: 19.03.1984

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  mathscinet  zmath
    2. Zavialov B., “On the Asymptotic Properties of Functions Holomorphic in Tubular Cones”, 294, no. 5, 1987, 1048–1050  mathscinet  isi
    3. B. I. Zavialov, “On the asymptotic properties of functions holomorphic in tubular cones”, Math. USSR-Sb., 64:1 (1989), 97–113  mathnet  crossref  mathscinet  zmath
    4. Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Abelian and Tauberian comparison theorems”, Math. USSR-Sb., 68:1 (1991), 85–110  mathnet  crossref  mathscinet  zmath  isi
    5. A. L. Yakymiv, “Tauberian theorems and asymptotics of infinitely divisible distributions in a cone”, Theory Probab. Appl., 48:3 (2004), 493–505  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. A. L. Yakymiv, “Admissible Functions for the Positive Octant”, Math. Notes, 76:3 (2004), 432–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. J., 7:3 (2015), 47–53  mathnet  crossref  mathscinet  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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