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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 1(5), Pages 97–114 (Mi msb1730)  

This article is cited in 8 scientific papers (total in 8 papers)

On the asymptotic properties of functions holomorphic in tubular cones

B. I. Zavialov


Abstract: For functions holomorphic in tube domains over a cone, the author studies the connection between their asymptotic behavior at the origin along orbits of one-parameter groups of linear transformations and asymptotic properties of the real parts of the boundary values of these functions. It is shown that, as a rule, the presence of certain asymptotics of the real part of a boundary value of a holomorphic function guarantees similar asymptotics for the whole function within the domain.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:1, 97–113

Bibliographic databases:

Document Type: Article
UDC: 517.5
MSC: Primary 32A10, 32A07; Secondary 32A40, 46F20
Received: 02.04.1987

Citation: B. I. Zavialov, “On the asymptotic properties of functions holomorphic in tubular cones”, Mat. Sb. (N.S.), 136(178):1(5) (1988), 97–114; Math. USSR-Sb., 64:1 (1989), 97–113

Citation in format AMSBIB
\Bibitem{Zav88}
\by B.~I.~Zavialov
\paper On the asymptotic properties of functions holomorphic in tubular cones
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 1(5)
\pages 97--114
\mathnet{http://mi.mathnet.ru/msb1730}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=945902}
\zmath{https://zbmath.org/?q=an:0668.32003|0652.32003}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 97--113
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003296}


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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, “A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the positive octant”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 185–209  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. Nikolicdespotovic D., Pilipovic S., “The Quasiasymptotic Expansion at the Origin - Abelian-Type Results for Laplace and Stieltjes Transforms”, Math. Nachr., 174 (1995), 231–238  crossref  mathscinet  isi
    4. Yu. N. Drozhzhinov, B. I. Zavialov, “Local Tauberian theorems in spaces of distributions related to cones, and their applications”, Izv. Math., 61:6 (1997), 1171–1214  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Pilipovic S., Stojanovic M., “On the Behaviour of Colombeau's Generalized Functions at a Point - Applications to Semilinear Systems”, Publ. Math.-Debr., 51:1-2 (1997), 111–126  mathscinet  zmath  isi
    6. Pilipovic S. Vindas J., “Multidimensional Tauberian Theorems For Vector-Valued Distributions”, Publ. Inst. Math.-Beograd, 95:109 (2014), 1–28  crossref  isi
    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
    8. S. Pilipović, J. Vindas, “Tauberian class estimates for vector-valued distributions”, Sb. Math., 210:2 (2019), 272–296  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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