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

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:

UDC: 517.53
MSC: Primary 46F12; Secondary 44A10, 40E05

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
\Bibitem{DroZav89} \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 \mathnet{http://mi.mathnet.ru/msb1658} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1017823} \zmath{https://zbmath.org/?q=an:0736.46032} \transl \jour Math. USSR-Sb. \yr 1991 \vol 68 \issue 1 \pages 85--110 \crossref{https://doi.org/10.1070/SM1991v068n01ABEH001197} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991EX22700005} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. K. Kh. Boimatov, “Multidimensional spectral asymptotics for elliptic differential operators”, Russian Math. Surveys, 46:3 (1991), 213–214
3. Boimatov K., “Multidimensional Spectral Asymptotics for Elliptic-Operators on Domains Satisfying the Cone Condition”, 316, no. 1, 1991, 14–18
4. Boimatov K., “Multiparametric Spectral Asymptotic for Elliptic-Systems of Differential-Operators on Arbitrary Domains of Finite Measure”, 321, no. 6, 1991, 1138–1142
5. Boimatov K., “Multi-Parametric Spectral Asymptotics for Elliptic Pseudodifferential-Operators on Compact Manifolds”, 319, no. 5, 1991, 1048–1052
6. Boimatov K., “Multidimensional Distribution-Functions for Degenerate Elliptic-Operators”, 317, no. 2, 1991, 271–275
7. K. Kh. Boimatov, “Multidimensional Distribution Functions for Elliptic Operators”, Funct. Anal. Appl., 27:4 (1993), 273–275
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
9. Boimatov K., “Asymptotic Behavior of the Eigenvalue Distribution Function for Elliptic Operators in R-N”, Dokl. Akad. Nauk, 358:6 (1998), 729–730
10. Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. J., 7:3 (2015), 47–53
11. A. L. Yakymiv, “A Tauberian theorem for multiple power series”, Sb. Math., 207:2 (2016), 286–313
12. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134
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