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Mat. Sb., 1989, Volume 180, Number 9, Pages 1234–1258 (Mi msb1658)  

This article is cited in 12 scientific papers (total in 12 papers)

Multidimensional Abelian and Tauberian comparison theorems

Yu. N. Drozhzhinov, B. I. Zavialov

Abstract: Theorems in which a specified asymptotic behavior of the quotient of two (generalized) functions leads to a conclusion about the asymptotic behavior of the quotient of integral transforms of them are called Abelian comparison theorems. The theorems converse to them are called Tauberian comparison theorems. This article concerns some Abelian and Tauberian comparison theorems for generalized functions with supports in pointed cones. The Laplace transform is used as an integral transform. It is shown that additional “Abelian” conditions are needed for the validity of Abelian theorems in the multidimensional case.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Sbornik, 1991, 68:1, 85–110

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: Primary 46F12; Secondary 44A10, 40E05
Received: 03.10.1988

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Abelian and Tauberian comparison theorems”, Mat. Sb., 180:9 (1989), 1234–1258; Math. USSR-Sb., 68:1 (1991), 85–110

Citation in format AMSBIB
\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper Multidimensional Abelian and Tauberian comparison theorems
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 9
\pages 1234--1258
\jour Math. USSR-Sb.
\yr 1991
\vol 68
\issue 1
\pages 85--110

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    This publication is cited in the following articles:
    1. Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional tauberian comparison theorems for holomorphic functions of bounded argument”, Math. USSR-Izv., 39:3 (1992), 1097–1112  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. K. Kh. Boimatov, “Multidimensional spectral asymptotics for elliptic differential operators”, Russian Math. Surveys, 46:3 (1991), 213–214  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Boimatov K., “Multidimensional Spectral Asymptotics for Elliptic-Operators on Domains Satisfying the Cone Condition”, 316, no. 1, 1991, 14–18  mathscinet  isi
    4. Boimatov K., “Multiparametric Spectral Asymptotic for Elliptic-Systems of Differential-Operators on Arbitrary Domains of Finite Measure”, 321, no. 6, 1991, 1138–1142  mathscinet  isi
    5. Boimatov K., “Multi-Parametric Spectral Asymptotics for Elliptic Pseudodifferential-Operators on Compact Manifolds”, 319, no. 5, 1991, 1048–1052  mathscinet  isi
    6. Boimatov K., “Multidimensional Distribution-Functions for Degenerate Elliptic-Operators”, 317, no. 2, 1991, 271–275  mathscinet  isi
    7. K. Kh. Boimatov, “Multidimensional Distribution Functions for Elliptic Operators”, Funct. Anal. Appl., 27:4 (1993), 273–275  mathnet  crossref  mathscinet  zmath  isi
    8. Boimatov K., “On the Asymptotic Behavior of the Mean Distribution Function for Elliptic Systems of Almost-Periodic Operators”, Dokl. Akad. Nauk, 362:6 (1998), 729–732  mathnet  mathscinet  zmath  isi
    9. Boimatov K., “Asymptotic Behavior of the Eigenvalue Distribution Function for Elliptic Operators in R-N”, Dokl. Akad. Nauk, 358:6 (1998), 729–730  mathnet  mathscinet  zmath  isi
    10. 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
    11. A. L. Yakymiv, “A Tauberian theorem for multiple power series”, Sb. Math., 207:2 (2016), 286–313  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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