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Mat. Sb., 1998, Volume 189, Number 7, Pages 91–130 (Mi msb333)  

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

A Wiener-type Tauberian theorem for generalized functions of slow growth

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper is devoted to the extension of Wiener-type Tauberian theorems to the case of generalized functions of slow growth. A functional is shown to have asymptotics (in the weak sense) if and only if it has asymptotics on a 'test' function whose Mellin transform is bounded away from zero in a certain strip of the complex plane related to the order of the functional in question. Applications of this result are also considered; in particular, several theorems on the lack of compensation of the singularities of holomorphic functions are proved.

DOI: https://doi.org/10.4213/sm333

Full text: PDF file (474 kB)
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English version:
Sbornik: Mathematics, 1998, 189:7, 1047–1086

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: Primary 46E12; Secondary 40E05
Received: 18.09.1997

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “A Wiener-type Tauberian theorem for generalized functions of slow growth”, Mat. Sb., 189:7 (1998), 91–130; Sb. Math., 189:7 (1998), 1047–1086

Citation in format AMSBIB
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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. Drozhzhinov, YN, “Wiener type Tauberian theorems for generalized functions and Stieltjes transform”, Doklady Akademii Nauk, 363:2 (1998), 156  mathnet  mathscinet  zmath  isi
    2. Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorem for generalized multiplicative convolutions”, Izv. Math., 64:1 (2000), 35–92  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Yu. N. Drozhzhinov, B. I. Zavialov, “Wiener-Type Tauberian Theorems for Generalized Functions on the Half-Axis”, Proc. Steklov Inst. Math., 228 (2000), 43–51  mathnet  mathscinet  zmath
    4. Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorems for generalized functions with values in Banach spaces”, Izv. Math., 66:4 (2002), 701–769  mathnet  crossref  crossref  mathscinet  zmath  elib
    5. Drozhzhinov, YN, “Tauberian theorems for distributions in the scale of regularly varying functionals”, Doklady Mathematics, 65:2 (2002), 180  mathscinet  zmath  isi  elib
    6. Yu. N. Drozhzhinov, B. I. Zavialov, “Applications of Tauberian theorems in some problems in mathematical physics”, Theoret. and Math. Phys., 157:3 (2008), 1678–1693  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. 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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