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Mat. Sb. (N.S.), 1979, Volume 108(150), Number 1, Pages 78–90 (Mi msb2264)  

This article is cited in 16 scientific papers (total in 16 papers)

Tauberian theorems for generalized functions with supports in cones

Yu. N. Drozhzhinov, B. I. Zavialov

Abstract: In this article the authors prove several multidimensional theorems of Tauberian type, connecting the behavior at infinity of generalized functions with support in a cone with the behavior of their Fourier–Laplace transforms in a neighborhood of zero. As corollaries they deduce a strengthened version of V. S. Vladimirov's Tauberian theorem and an analog of the theorem of Lindelöf for the edge of a tube domain over a cone.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Sbornik, 1980, 36:1, 75–86

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: Primary 46F12; Secondary 46F20
Received: 06.03.1978

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorems for generalized functions with supports in cones”, Mat. Sb. (N.S.), 108(150):1 (1979), 78–90; Math. USSR-Sb., 36:1 (1980), 75–86

Citation in format AMSBIB
\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper Tauberian theorems for generalized functions with supports in~cones
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 108(150)
\issue 1
\pages 78--90
\jour Math. USSR-Sb.
\yr 1980
\vol 36
\issue 1
\pages 75--86

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    This publication is cited in the following articles:
    1. K. A. Bukin, “Asymptotic behavior of the two-point Wightman function”, Theoret. and Math. Phys., 40:1 (1979), 581–587  mathnet  crossref  mathscinet  isi
    2. V. V. Zharinov, “Quasiasymptotic behavior of Fourier hyperfunctions”, Theoret. and Math. Phys., 43:1 (1980), 302–306  mathnet  crossref  mathscinet  zmath  isi
    3. A. L. Yakymiv, “Multidimensional Tauberian theorems and their application to Bellman–Harris branching processes”, Math. USSR-Sb., 43:3 (1982), 413–425  mathnet  crossref  mathscinet  zmath
    4. Drozhzhinov I., “Tauber Multidimensional Theorem for Holomorphic-Functions with Nonnegative Imaginary Part”, 258, no. 3, 1981, 530–532  mathscinet  zmath  isi
    5. Yu. N. Drozhzhinov, “A multidimensional Tauberian theorem for holomorphic functions of bounded argument and the quasi-asymptotics of passive systems”, Math. USSR-Sb., 45:1 (1983), 45–61  mathnet  crossref  mathscinet  zmath
    6. Zavialov B. Drozhzhinov I., “A Multidimensional Analog of the Lindelof Theorem”, 262, no. 2, 1982, 269–270  mathscinet  isi
    7. S. M. Kozlov, “Multidimensional spectral asymptotics for elliptic operators in a bounded domain”, Math. USSR-Izv., 24:1 (1985), 49–71  mathnet  crossref  mathscinet  zmath
    8. Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotic properties of some classes of generalized functions”, Math. USSR-Izv., 26:1 (1986), 77–131  mathnet  crossref  mathscinet  zmath
    9. Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Tuberian comparison theorems for generalized functions in cones”, Math. USSR-Sb., 54:2 (1986), 499–524  mathnet  crossref  mathscinet  zmath
    10. B. Stanković, “Abelian and Tauberian theorems for Stieltjes transforms of distributions”, Russian Math. Surveys, 40:4 (1985), 99–113  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371  mathnet  crossref  mathscinet  zmath
    12. 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
    13. J. Schmeelk, A. Takači, “Quasiasymptotics and the dual Fock space”, Integral Transforms and Special Functions, 6:1-4 (1998), 309  crossref
    14. Markus Niemann, Ivan G. Szendro, Holger Kantz, “1/fβ noise in a model for weak ergodicity breaking”, Chemical Physics, 375:2-3 (2010), 370  crossref
    15. Pilipovic S., Vindas J., “Multidimensional Tauberian Theorems For Vector-Valued Distributions”, Publ. Inst. Math.-Beograd, 95:109 (2014), 1–28  crossref  isi
    16. 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
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