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Mat. Sb., 1994, Volume 185, Number 2, Pages 57–86 (Mi msb879)  

This article is cited in 3 scientific papers (total in 3 papers)

A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the positive octant

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper is devoted to a multidimensional Tauberian theorem of Hardy–Littlewood type for quasiasymptotic expansions of measures concentrated in the positive octant. Here the quasiasymptotic expansion is assumed to be local, i.e., its terms are generalized functions concentrated at the origin. The asymptotic behavior of the remainder is estimated with respect to the scale of regularly varying (self-similar) functions along trajectories defined by one-parameter groups of automorphisms of the cone in which the measure is concentrated. The case of one variable is investigated in more detail; in particular, a Hardy–Littlewood type theorem is proved for generalized functions that are nonnegative measures for large values of the argument.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 81:1, 185–209

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: Primary 28A35, 40E05; Secondary 46F12
Received: 02.06.1993

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the positive octant”, Mat. Sb., 185:2 (1994), 57–86; Russian Acad. Sci. Sb. Math., 81:1 (1995), 185–209

Citation in format AMSBIB
\Bibitem{DroZav94}
\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the~positive octant
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 2
\pages 57--86
\mathnet{http://mi.mathnet.ru/msb879}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1264774}
\zmath{https://zbmath.org/?q=an:0834.40003}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 81
\issue 1
\pages 185--209
\crossref{https://doi.org/10.1070/SM1995v081n01ABEH003620}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995QZ14400010}


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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. Yu. N. Drozhzhinov, B. I. Zavialov, “Theorems of Hardy–Littlewood type for signed measures on a cone”, Sb. Math., 186:5 (1995), 675–693  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. 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 - 1992–2005 Sbornik: Mathematics (from 1967)
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