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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 6, Pages 59–102 (Mi izv165)  

This article is cited in 2 scientific papers (total in 2 papers)

Local Tauberian theorems in spaces of distributions related to cones, and their applications

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this article we introduce and study special spaces of distributions related to a given cone. These spaces occupy an intermediate position between the space of temperate distributions and the class of distributions concentrated on a cone. The properties of these spaces are investigated. In particular, we prove that they are convolution algebras. Quasi-asymptotic properties of distributions belonging to these spaces are thoroughly studied. To this end we prove several complex Tauberian and Abelian theorems in which the role of the integral transformation is played by the Laplace transformation. This transformation establishes an isomorphism between these spaces and the classes of functions holomorphic in special wedge-shaped domains. These results are applied to the study of the asymptotic behaviour of functions holomorphic in wedge-shaped domains at boundary points. A local theorem on non-compensation of singularities of holomorphic functions is proved.

DOI: https://doi.org/10.4213/im165

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English version:
Izvestiya: Mathematics, 1997, 61:6, 1171–1214

Bibliographic databases:

Document Type: Article
MSC: 40E05, 32A40, 46F12
Received: 11.03.1996

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Local Tauberian theorems in spaces of distributions related to cones, and their applications”, Izv. RAN. Ser. Mat., 61:6 (1997), 59–102; Izv. Math., 61:6 (1997), 1171–1214

Citation in format AMSBIB
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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. 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
    2. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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