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Mathematics of the USSR-Sbornik, 1991, Volume 68, Issue 1, Pages 85–110
DOI: https://doi.org/10.1070/SM1991v068n01ABEH001197 (Mi sm1658) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Multidimensional Abelian and Tauberian comparison theorems

Yu. N. Drozhzhinov, B. I. Zavialov
English version PDF (1017 kB) Citations (13)
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DOI: https://doi.org/10.1070/SM1991v068n01ABEH001197
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.
Received: 03.10.1988
Russian version:
Matematicheskii Sbornik, 1989, Volume 180, Number 9, Pages 1234–1258
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 46F12; Secondary 44A10, 40E05
Language: English
Original paper language: Russian
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
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\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
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\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991EX22700005}
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  • https://doi.org/10.1070/SM1991v068n01ABEH001197
  • https://www.mathnet.ru/eng/sm/v180/i9/p1234
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник - 1989–1990 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:335
    Russian version PDF:110
    English version PDF:13
    References:57
    First page:2
     
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